What is ordering decimals, place values chart in decimals, different types of ordering, solved examples on ordering decimals, practice problems on ordering decimals, frequently asked questions on ordering decimals.
Arranging decimal numbers in a specific order, i.e, ascending or descending, on the basis of the place values is known as ordering decimals.
Decimals are numbers that have a whole number part and a fractional part divided by a decimal point. Decimals just like any other numbers can be compared and ordered in either ascending or descending order.
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Comparing and ordering decimals gets easier with the place value chart. The following image shows the place value chart in decimals.
Let’s understand the place values of decimals with an example. Consider the decimal number 1111.1111. Every place has the same digit. However, their place values are different!
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Steps of Ordering Decimals
To order decimal numbers, we need to first learn how to compare decimal numbers.
Step 1: Use the place value chart!
Write the decimals in the place value chart such that the place values of all the decimals are aligned. The empty boxes at the end of the decimal can be filled with zeroes.
Step 2: Compare the whole number part first.
Always start comparing the digits at the highest place value. Thus, the decimal having the greater whole number part is greater!
For example: Consider the decimals 12.5 and 15.2.
12 is less than 15
Thus, 15.2 is greater than 12.5.
Step 3: Compare the tenths!
If the whole number part matches, compare the next place value, tenth.
Consider the decimals 1.5 and 1.4.
The whole number is 1 in both numbers, thus we will compare the digits after the decimal point—4 and 5.
Thus, $1.5 \gt 1.4$
Step 4: Compare the hundredths.
If the digits at the tenth place are the same, move to the next place value and compare the digits.
Example: Consider the decimals 23.56 and 23.53.
We will write them in the place value chart for better understanding!
The part 23.5 is the same in both the decimals.
Thus, we compare the digits at the hundredths place, 3 and 6.
$3 \gt 6$ and hence 23.56 is greater than 23.53.
Once you compare the given decimals, ordering them is just the matter of arranging them in increasing or decreasing order.
There are two different types of the ordering of decimals:
Ascending order: The order of decimal numbers such that, in a sequence, each decimal number is not less than the previous number, or we can also say that the terms are either equal or greater than the previous number.
Descending order: The order of decimal numbers such that, in a sequence, each decimal number is not more than the previous number, or we can also say that the terms are either equal or lesser than the previous number.
How to Order Decimals
To order decimals, we will first compare the decimals. Write the decimals in the place value chart in order to compare them. To arrange them in ascending order, we write them from the smallest to the greatest. To arrange them in descending order, we write them from the greatest to the smallest.
Example 1: Order decimals from least to greatest.
5.31, 6.88, 7.21, 6.45
Compare the digits at ones place: we get $7 \gt 6 \gt 5$
Thus, 7.21 is the greatest decimal and 5.31 is the smallest.
To compare 6.88 and 6.45, compare the digits at the tenths place.
Since $4 \lt 8$, we get $6.45 \lt 6.88$
Thus, $5.31 \lt 6.45 \lt 6.88 \lt 7.21$
The given decimals can be arranged in ascending order as: 5.31, 6.45, 6.88, 7.21
Ordering Decimals in Ascending Order
To order the decimal numbers in ascending order, we will arrange the numbers in such a way that each decimal number is smaller than the next decimal number. It means increasing order. How can we order decimals from least to greatest? Simply compare them using the place value chart and start listing them in the increasing order.
Ordering Decimals in Descending Order
To order the decimal numbers in descending order, we will arrange the numbers in such a way that each decimal number is larger than the next decimal number. It means decreasing order.
The decimal numbers are of three types—terminating, non-terminating repeating, and non-terminating non-repeating.
The terminating and non-terminating repeating decimal numbers are classified as rational numbers.
The non-terminating non-repeating decimal numbers are classified as irrational numbers.
This article gives an insight into the concept of decimals, teaching us how to compare decimals and how to arrange them in ascending or descending order. Ordering decimals is a part of daily life, which we see commonly while comparing amounts of some objects and the values are in decimal numbers.
1. Compare and arrange the following decimal numbers in descending order:
0.51, 0.45, 3.22, 1.67, 0.452.
Solution:
Write the numbers in the place value chart. Start comparing the digits at the highest place value, that is, the ones place.
Comparing the ones place digits, we get
$1.67 \lt 3.22$
For the decimals 0.51, 0.45, and 0.452, we compare the tenths, hundredths, and thousandths place.
$0.51 \lt 0.450 \lt 0.452$
The numbers in descending order are:
$3.22 \gt 1.67 \gt 0.51 \gt 0.452 \gt 0.45$
2. Which one is greater—1.01 or 1.10?
The numbers 1.01 and 1.10 both have the same whole number part 1.
We will compare the digits at the tenths place, which are 0 and 1.
Thus $1.10 \gt 1.01$.
3. Arrange the given decimals in ascending order.
0.96, 6.01, 0.0009, 0.93
Solution: Start comparing the digits at the highest place value.
We get that 6.01 is the greatest decimal.
Between 0.96, 0.93 and 0.0009, we get
$0.93 \lt 0.96 \lt 0.0009$
Thus, the given decimals can be written in the ascending order as:
$0.93 \lt 0.96 \lt 0.0009 \lt 6.01$
Attend this quiz & Test your knowledge.
Which one of the following is the same as 1.1?
Which of the following represents an ascending order of decimal numbers, which one of the following decimals is the smallest, choose the correct sign. 0.119 ____ 0.091.
What are terminating decimal numbers?
Terminating decimal numbers are numbers that have a finite number of digits after the decimal point, and they terminate after certain decimal places. For example, 0.5, 1.2345, etc.
What is the significance of ordering?
Ordering is an important part of life. Without ordering, analysis of sufficiently large data is almost impossible. We see ordering in almost every part of our life, like the order of events in a party, the order of items on a shelf, etc.
What are rational numbers in terms of decimals?
Rational numbers are numbers that have either terminating or non-terminating repeating decimal forms. These numbers can be represented as a fraction where the denominator is non-zero.
What are decimal fractions?
Decimal fractions are fractions whose denominator is a power of 10.
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Ordering Decimals Worksheets
This webpage encompasses a combination of printable worksheets based on ordering decimals with a view to enhance 4th grade and 5th grade students' knowledge on decimals and their place values. A number of pdf worksheets are stacked with a variety of exercises include ordering decimals in place value boxes, using the number line, and using the greater than and less than symbols. Riddle worksheets require you to order decimals to decode the riddles that are sure to tickle your funny bone! Our free ordering decimal worksheets are perfect launchpads!
Ordering Decimals - Standard | Level 1
Observe the digits in the whole number and decimal parts and order each set of decimals in either increasing or decreasing order as directed. Level 1 involves up to hundredths decimal places.
Download the set
Ordering Decimals: Number Lines
Read the number line. Arrange each set of decimals in either increasing or decreasing order as specified. Rule: Decimals to the right of the number line will always be greater than the decimals to the left of it.
Ordering Decimals: Greater Than and Less Than Symbols
Decimal numbers are given in random order. Set them in the correct order in accordance with the greater than and less than symbols provided. There are seven problems in each pdf worksheet for grade 4 and grade 5.
Ordering Decimals - Standard | Level 2
Levitate your ordering practice with these worksheets featuring decimals with up to thousandths places. Write the decimals in the ascending order in part A and the descending order in part B.
Ordering Decimals: Place Value Boxes
Keenly observe each set of decimals and fill them in the correct place value boxes provided. Order the decimals from the least to the greatest and vice versa.
Ordering Decimals: Increasing Order Riddles
Read each decimal number displayed on these vivid theme-based pdf worksheets. Order them in the increasing order and decode the rib-tickling riddles!
Ordering Decimals: Decreasing Order Riddles
Grade 4 and grade 5 children are expected to figure out the largest decimal and move on till the smallest one; write down the corresponding letters; solve the intriguing riddles.
Ordering Decimals: MCQs
Identify the correct sequence of decimals in either increasing or decreasing order with this set of MCQs. This activity forms a perfect tool in evaluating a child's analytical and logical skills.
Ordering Decimals - Standard | Level 3
Transcend your peers in ordering decimals with these level 3 worksheets. Swap the positions of the numbers incorporating up to ten thousandths places and arrange them in the indicated order.
Comparing Decimals Worksheets
This assortment of 60+ worksheets consists of captivating exercises and activities on comparing decimals using greater than, lesser than and equal to symbols.
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Ordering Decimals - Grid Puzzles
Subject: Mathematics
Age range: 7-11
Resource type: Worksheet/Activity
Last updated
16 September 2022
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A Bronze/Silver/Gold differentiated resource where pupils are given a list of decimals and a square grid. Pupils have to put the decimals into the grid so that each row and column is in ascending order.
In Bronze, the integer part of each decimal is the same. In Silver, the integer parts are different. In Gold, negatives are introduced. The grids get progressively larger as you move from Bronze to Gold as well.
Each puzzle has multiple solutions, but I’ve provided one possible solution to each.
Update 16/9/22: Changed the design of the tasks, but the content is the same.
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Order Decimal Numbers — Online Practice Game (grades 4-7)
Practice ordering decimals (from the smallest to the greatest) by dragging them into "boxes" in the correct order. You can choose to order either 3 or 4 decimals.
You can also choose the number of decimal digits for the numbers. For example, students in 4th grade might use decimals with two decimal digits, and students in 5th grade decimals with three decimal digits (places). [Mobile users]: You might have to turn your phone landscape to get the decimals to fit.
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Ordering Decimals Lesson
Example 1: The Glosser Family drove to a gasoline station in their neighborhood. The station has three gas pumps, each marked in price per gallon. Which pump has the lowest price per gallon? Which pump has the highest price per gallon?
$1.79, $1.96, $1.61
Analysis: We know that 1.79 < 1.96 and that 1.79 > 1.61. Writing one decimal beneath the other in order, we get:
1
.
6
1
1
.
7
9
1
.
9
6
Answer: The pump marked $1.61 has the lowest price per gallon. The pump marked $1.96 has the highest price per gallon.
In the example above, we ordered three decimal numbers from least to greatest by comparing them two at a time. Let’s look at some more examples.
Example 2: Order these decimals from least to greatest: 0.5629, 0.5621, 0.6521
Let’s examine these decimals in our place-value-chart.
Now let’s order these decimals from least to greatest without our place-value chart. We will do this by comparing two decimals at a time.
0
.
5
6
2
1
0
.
5
6
2
9
0
.
6
5
2
1
Answer: Ordering these decimals from least to greatest we get: 0.5621, 0.5629, 0.6521.
In the examples above, the decimals in each problem had the same number of digits. Thus, they lined up nicely, one beneath the other. Let’s look at some examples in which the decimals presented have a different number of decimal digits.
Example 3: Order these decimals from least to greatest: 6.01, 0.601, 6.1
Let’s start by writing one decimal beneath the other in their original order. Note that these three decimals have a different number of decimal digits.
6
.
0
1
0
.
6
0
1
6
.
1
Next, examine each decimal, writing one or more zeros to the right of the last digit, so that all decimals have the same number of decimal digits.
6
.
0
1
0
0
.
6
0
1
6
.
1
0
0
Now we can compare two decimals at a time.
From least to greatest, we get: 0.6010, 6.010, 6.100.
Answer: Ordering these decimals from least to greatest we get: 0.601, 6.01, 6.1.
Sometimes it is helpful to place a number in a circle to the right of each decimal you are trying to order. This is done in Example 4.
Example 4: Order these decimals from least to greatest: 3.87, 3.0875, 3.87502, 3.807
We have been asked to order four decimal numbers. Let’s start by writing one decimal beneath the other in their original order.
3
.
8
7
3
.
0
8
7
5
3
.
8
7
5
0
2
3
.
8
0
7
3
.
8
7
0
0
0
3
.
0
8
7
5
0
3
.
8
7
5
0
2
3
.
8
0
7
0
0
Now we can compare two decimals at a time. We will write a number in a circle next to each decimal to denote its order.
3
.
8
7
0
0
0
3
.
0
8
7
5
0
3
.
8
7
5
0
2
3
.
8
0
7
0
0
From least to greatest, we get: 3.08750, 3.80700, 3.87000, 3.87502
Answer: Ordering these decimals from least to greatest we get: 3.0875, 3.807, 3.87, 3.87502
Example 5: Order these decimals from least to greatest: 5.364, 6.0364, 5.36, 5.00364, 5.40364
We have been asked to order five decimal numbers. Let’s start by writing one decimal beneath the other in their original order. Next, examine each decimal, writing one or more zeros to the right of the last digit, as needed.
5
.
3
6
4
0
0
6
.
0
3
6
4
0
5
.
3
6
0
0
0
5
.
0
0
3
6
4
5
.
4
0
3
6
4
5
.
3
6
4
0
0
6
.
0
3
6
4
0
5
.
3
6
0
0
0
5
.
0
0
3
6
4
5
.
4
0
3
6
4
From least to greatest, we get: 5.00364, 5.36000, 5.36400, 5.40364, 6.03640
Answer: Ordering these decimals from least to greatest we get: 5.00364, 5.36, 5.364, 5.40364, 6.0364
Let’s look at some non-routine problems that involve comparing and ordering decimals.
Example 6: Write 3 decimals between 4.35 and 4.36 in order from least to greatest.
Analysis: We need to write a zero in the thousandths place for each of the given numbers.
4
.
3
5
0
4
.
3
6
0
4
.
3
5
0
4
.
3
6
0
Sample Answer 1: 4.351, 4.352, 4.353
Sample Answer 2: 4.354, 4.356, 4.358
Example 7: Write 3 decimals between 7.418 and 7.419 in order from least to greatest.
Analysis: We need to write a zero in the ten-thousandths place for each of the given numbers.
7
.
4
1
8
0
7
.
4
1
9
0
7
.
4
1
8
0
7
.
4
1
9
0
Sample Answer 1: 7 .4182, 7.4183, 7.4184
Sample Answer 2: 7 .4185, 7.4187, 7.4189
Example 8: Write the smallest possible decimal between zero and one that uses the digits 5, 0, 4, 1, 9, and 6 exactly once.
Answer: .014569. Note that a leading zero was not used here.
Example 9: Write the greatest possible decimal between zero and one that uses the digits 9, 0, 2, 7, 3 and 5 exactly once.
Answer: .975320 (without a leading zero) or 0.97532 (with a leading zero). Note that these two decimals are equivalent.
Summary: When ordering decimals, first write one decimal beneath the other in their original order. Then compare them two at a time. When ordering four or more decimals, it is helpful to write a number in a circle next to each to order them.
Directions: Read each question below. You may use paper to help you find the answers. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, choose a different button.
RESULTS BOX:
RESULTS BOX:
0.910, 0.091, 0.9?
RESULTS BOX:
3.45, 3.0459, 3.5, 3.4059?
RESULTS BOX:
Variation Theory
Sequences and behaviour to enable mathematical thinking in the classroom - by craig barton @mrbartonmaths.
Ordering decimals
Author: Jess Prior
This type of activity is known as Practice . Please read the guidance notes here , where you will find useful information for running these types of activities with your students.
1. Example-Problem Pair
2. Intelligent Practice
4. Downloadable version
Ordering decimals – PowerPoint
ordering decimals – worksheet
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Inspiration
Ordering Decimals
Related Topics & Worksheets: Ordering Decimals
Objective: I can put decimals in order.
To write decimals from least to greatest and vice versa, we need to first compare the decimals two at a time.
Example: Order the decimals
1.243, 0.243, and 1.24
Solution: Step 1: Compare the decimals two at a time.
1.243 > 1.24
1.24 > 0.243
Step 2: List the decimals from least to greatest.
0.243, 1.24, 1.243
We hope that the free math worksheets have been helpful. We encourage parents and teachers to select the topics according to the needs of the child. For more difficult questions, the child may be encouraged to work out the problem on a piece of paper before entering the solution. We hope that the kids will also love the fun stuff and puzzles.
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Decimal Worksheets Hub Page
Welcome to our Decimal Worksheets area.
On this page, there are links to all of our decimal math worksheets, including decimal place value, decimal money worksheets and our adding, subtracting, multiplying and dividing decimals pages.
We also have some decimal resources including decimal place value charts to support teaching and learning of decimals.
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Decimal Worksheets
On this page you will find link to our range of decimal math worksheets.
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Decimal Place Value Charts
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These decimal place value charts are designed to help children understand decimal place value.
They are especially useful in learning how to multiply and divide decimals by 10 or 100.
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Here you will find our selection of Place Value involving Decimals with up to 2 decimal places (2dp).
Using these sheets will help your child learn to:
learn their place value with decimals up to 3dp;
understand the value of each digit in a decimal number;
learn to read and write numbers with up to 3dp.
Decimal Place Value Worksheets to 2dp
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Using these sheets will support you child to:
count on and back by multiples of 0.1;
fill in the missing numbers in sequences;
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Thanks for visiting the Decimals Worksheets page at Math-Drills.Com where we make a POINT of helping students learn. On this page, you will find Decimals worksheets on a variety of topics including comparing and sorting decimals, adding, subtracting, multiplying and dividing decimals, and converting decimals to other number formats. To start, you will find the general use printables to be helpful in teaching the concepts of decimals and place value. More information on them is included just under the sub-title.
Further down the page, rounding, comparing and ordering decimals worksheets allow students to gain more comfort with decimals before they move on to performing operations with decimals. There are many operations with decimals worksheets throughout the page. It would be a really good idea for students to have a strong knowledge of addition, subtraction, multiplication and division before attempting these questions.
Most Popular Decimals Worksheets this Week
Grids and Charts Useful for Learning Decimals
General use decimal printables are used in a variety of contexts and assist students in completing math questions related to decimals.
The thousandths grid is a useful tool in representing decimals. Each small rectangle represents a thousandth. Each square represents a hundredth. Each row or column represents a tenth. The entire grid represents one whole. The hundredths grid can be used to model percents or decimals. The decimal place value chart is a tool used with students who are first learning place value related to decimals or for those students who have difficulty with place value when working with decimals.
Thousandths and Hundredths Grids Thousandths Grid Hundredths Grids ( 4 on a page) Hundredths Grids ( 9 on a page) Hundredths Grids ( 20 on a page)
Decimal Place Value Charts Decimal Place Value Chart ( Ones to Hundredths ) Decimal Place Value Chart ( Ones to Thousandths ) Decimal Place Value Chart ( Hundreds to Hundredths ) Decimal Place Value Chart ( Thousands to Thousandths ) Decimal Place Value Chart ( Hundred Thousands to Thousandths ) Decimal Place Value Chart ( Hundred Millions to Millionths )
Decimals in Expanded Form
For students who have difficulty with expanded form, try familiarizing them with the decimal place value chart, and allow them to use it when converting standard form numbers to expanded form. There are actually five ways (two more than with integers) to write expanded form for decimals, and which one you use depends on your application or preference. Here is a quick summary of the various ways using the decimal number 1.23. 1. Expanded Form using decimals: 1 + 0.2 + 0.03 2. Expanded Form using fractions: 1 + 2 ⁄ 10 + 3 ⁄ 100 3. Expanded Factors Form using decimals: (1 × 1) + (2 × 0.1) + (3 × 0.01) 4. Expanded Factors Form using fractions: (1 × 1) + (2 × 1 ⁄ 10 ) + (3 × 1 ⁄ 100 ) 5. Expanded Exponential Form: (1 × 10 0 ) + (2 × 10 -1 ) + (3 × 10 -2 )
Converting Decimals from Standard Form to Expanded Form Using Decimals Converting Decimals from Standard to Expanded Form Using Decimals ( 3 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 4 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 5 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 6 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 7 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 8 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 9 Decimal Places)
Converting Decimals from Standard Form to Expanded Form Using Fractions Converting Decimals from Standard to Expanded Form Using Fractions ( 3 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 4 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 5 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 6 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 7 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 8 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 9 Decimal Places)
Converting Decimals from Standard Form to Expanded Factors Form Using Decimals Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 3 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 4 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 5 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 6 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 7 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 8 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 9 Decimal Places)
Converting Decimals from Standard Form to Expanded Factors Form Using Fractions Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 3 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 4 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 5 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 6 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 7 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 8 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 9 Decimal Places)
Converting Decimals from Standard Form to Expanded Exponential Form Converting Decimals from Standard to Expanded Exponential Form ( 3 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 4 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 5 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 6 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 7 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 8 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 9 Decimal Places)
Retro Converting Decimals from Standard Form to Expanded Form Retro Standard to Expanded Form (3 digits before decimal; 2 after) Retro Standard to Expanded Form (4 digits before decimal; 3 after) Retro Standard to Expanded Form (6 digits before decimal; 4 after) Retro Standard to Expanded Form (12 digits before decimal; 3 after)
Retro European Format Converting Decimals from Standard Form to Expanded Form Standard to Expanded Form (3 digits before decimal; 2 after) Standard to Expanded Form (4 digits before decimal; 3 after) Standard to Expanded Form (6 digits before decimal; 4 after)
Of course, being able to convert numbers already in expanded form to standard form is also important. All five versions of decimal expanded form are included in these worksheets.
Converting Decimals to Standard Form from Expanded Form Using Decimals Converting Decimals from Expanded Form Using Decimals to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 9 Decimal Places)
Converting Decimals to Standard Form from Expanded Form Using Fractions Converting Decimals from Expanded Form Using Fractions to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 9 Decimal Places)
Converting Decimals to Standard Form from Expanded Factors Form Using Decimals Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 9 Decimal Places)
Converting Decimals to Standard Form from Expanded Factors Form Using Fractions Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 9 Decimal Places)
Converting Decimals to Standard Form from Expanded Exponential Form Converting Decimals from Expanded Exponential Form to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 9 Decimal Places)
Retro Converting Decimals to Standard Form from Expanded Form Retro Expanded to Standard Form (3 digits before decimal; 2 after) Retro Expanded to Standard Form (4 digits before decimal; 3 after) Retro Expanded to Standard Form (6 digits before decimal; 4 after) Retro Expanded to Standard Form (12 digits before decimal; 3 after)
Retro European Format Converting Decimals to Standard Form from Expanded Form Retro European Format Expanded to Standard Form (3 digits before decimal; 2 after) Retro European Format Expanded to Standard Form (4 digits before decimal; 3 after) Retro European Format Expanded to Standard Form (6 digits before decimal; 4 after)
Rounding Decimals Worksheets
Rounding decimals is similar to rounding whole numbers; you have to know your place value! When learning about rounding, it is also useful to learn about truncating since it may help students to round properly. A simple strategy for rounding involves truncating, using the digits after the truncation to determine whether the new terminating digit remains the same or gets incremented, then taking action by incrementing if necessary and throwing away the rest. Here is a simple example: Round 4.567 to the nearest tenth. First, truncate the number after the tenths place 4.5|67. Next, look at the truncated part (67). Is it more than half way to 99 (i.e. 50 or more)? It is, so the decision will be to increment. Lastly, increment the tenths value by 1 to get 4.6. Of course, the situation gets a little more complicated if the terminating digit is a 9. In that case, some regrouping might be necessary. For example: Round 6.959 to the nearest tenth. Truncate: 6.9|59. Decide to increment since 59 is more than half way to 99. Incrementing results in the necessity to regroup the tenths into an extra one whole, so the result is 7.0. Watch that students do not write 6.10. You will want to correct them right away in that case. One last note: if there are three truncated digits then the question becomes is the number more than half way to 999. Likewise, for one digit; is the number more than half way to 9. And so on...
We should also mention that in some scientific and mathematical "circles," rounding is slightly different "on a 5". For example, most people would round up on a 5 such as: 6.5 --> 7; 3.555 --> 3.56; 0.60500 --> 0.61; etc. A different way to round on a 5, however, is to round to the nearest even number, so 5.5 would be rounded up to 6, but 8.5 would be rounded down to 8. The main reason for this is not to skew the results of a large number of rounding events. If you always round up on a 5, on average, you will have slightly higher results than you should. Because most pre-college students round up on a 5, that is what we have done in the worksheets that follow.
Rounding Decimals to Whole Numbers Round Tenths to a Whole Number Round Hundredths to a Whole Number Round Thousandths to a Whole Number Round Ten Thousandths to a Whole Number Round Various Decimals to a Whole Number
Rounding Decimals to Tenths Round Hundredths to Tenths Round Thousandths to Tenths Round Ten Thousandths to Tenths Round Various Decimals to Tenths
Rounding Decimals to Hundredths Round Thousandths to Hundredths Round Ten Thousandths to Hundredths Round Various Decimals to Hundredths
Rounding Decimals to Thousandths Round Ten Thousandths to Thousandths
Rounding Decimals to Various Decimal Places Round Hundredths to Various Decimal Places Round Thousandths to Various Decimal Places Round Ten Thousandths to Various Decimal Places Round Various Decimals to Various Decimal Places
European Format Rounding Decimals to Whole Numbers European Format Round Tenths to a Whole Number European Format Round Hundredths to a Whole Number European Format Round Thousandths to a Whole Number European Format Round Ten Thousandths to Whole Number
European Format Rounding Decimals to Tenths European Format Round Hundredths to Tenths European Format Round Thousandths to Tenths European Format Round Ten Thousandths to Tenths
European Format Rounding Decimals to Hundredths European Format Round Thousandths to Hundredths European Format Round Ten Thousandths to Hundredths
European Format Rounding Decimals to Thousandths European Format Round Ten Thousandths to Thousandths
Comparing and Ordering/Sorting Decimals Worksheets.
The comparing decimals worksheets have students compare pairs of numbers and the ordering decimals worksheets have students compare a list of numbers by sorting them.
Students who have mastered comparing whole numbers should find comparing decimals to be fairly easy. The easiest strategy is to compare the numbers before the decimal (the whole number part) first and only compare the decimal parts if the whole number parts are equal. These sorts of questions allow teachers/parents to get a good idea of whether students have grasped the concept of decimals or not. For example, if a student thinks that 4.93 is greater than 8.7, then they might need a little more instruction in place value. Close numbers means that some care was taken to make the numbers look similar. For example, they could be close in value, e.g. 3.3. and 3.4 or one of the digits might be changed as in 5.86 and 6.86.
Comparing Decimals up to Tenths Comparing Decimals up to Tenths ( Both Numbers Random ) Comparing Decimals up to Tenths ( One Digit Differs ) Comparing Decimals up to Tenths ( Both Numbers Close in Value ) Comparing Decimals up to Tenths ( Various Tricks )
Comparing Decimals up to Hundredths Comparing Decimals up to Hundredths ( Both Numbers Random ) Comparing Decimals up to Hundredths ( One Digit Differs ) Comparing Decimals up to Hundredths ( Two Digits Swapped ) Comparing Decimals up to Hundredths ( Both Numbers Close in Value ) Comparing Decimals up to Hundredths ( One Number has an Extra Digit ) Comparing Decimals up to Hundredths ( Various Tricks )
Comparing Decimals up to Thousandths Comparing Decimals up to Thousandths Comparing Decimals up to Thousandths ( One Digit Differs ) Comparing Decimals up to Thousandths ( Two Digits Swapped ) Comparing Decimals up to Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Thousandths ( Various Tricks )
Comparing Decimals up to Ten Thousandths Comparing Decimals up to Ten Thousandths Comparing Decimals up to Ten Thousandths ( One Digit Differs ) Comparing Decimals up to Ten Thousandths ( Two Digits Swapped ) Comparing Decimals up to Ten Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Ten Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Ten Thousandths ( Various Tricks )
Comparing Decimals up to Hundred Thousandths Comparing Decimals up to Hundred Thousandths Comparing Decimals up to Hundred Thousandths ( One Digit Differs ) Comparing Decimals up to Hundred Thousandths ( Two Digits Swapped ) Comparing Decimals up to Hundred Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Hundred Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Hundred Thousandths ( Various Tricks )
European Format Comparing Decimals European Format Comparing Decimals up to Tenths European Format Comparing Decimals up to Tenths (tight) European Format Comparing Decimals up to Hundredths European Format Comparing Decimals up to Hundredths (tight) European Format Comparing Decimals up to Thousandths European Format Comparing Decimals up to Thousandths (tight)
Ordering decimals is very much like comparing decimals except there are more than two numbers. Generally, students determine the least (or greatest) decimal to start, cross it off the list then repeat the process to find the next lowest/greatest until they get to the last number. Checking the list at the end is always a good idea.
European Format Ordering/Sorting Decimals European Format Ordering/Sorting Decimal Tenths (8 per set) European Format Ordering/Sorting Decimal Hundredths (8 per set) European Format Ordering/Sorting Decimal Thousandths (8 per set) European Format Ordering/Sorting Decimal Ten Thousandths (8 per set) European Format Ordering/Sorting Decimals with Various Decimal Places(8 per set)
Converting Decimals to Fractions and Other Number Formats
There are many good reasons for converting decimals to other number formats. Dealing with a fraction in arithmetic is often easier than the equivalent decimal. Consider 0.333... which is equivalent to 1/3. Multiplying 300 by 0.333... is difficult, but multiplying 300 by 1/3 is super easy! Students should be familiar with some of the more common fraction/decimal conversions, so they can switch back and forth as needed.
Converting Between Decimals and Fractions Converting Fractions to Terminating Decimals Converting Fractions to Terminating and Repeating Decimals Converting Terminating Decimals to Fractions Converting Terminating and Repeating Decimals to Fractions Converting Fractions to Hundredths
Converting Between Decimals, Fraction, Percents and Ratios Converting Fractions to Decimals, Percents and Part-to-Part Ratios Converting Fractions to Decimals, Percents and Part-to-Whole Ratios Converting Decimals to Fractions, Percents and Part-to-Part Ratios Converting Decimals to Fractions, Percents and Part-to-Whole Ratios Converting Percents to Fractions, Decimals and Part-to-Part Ratios Converting Percents to Fractions, Decimals and Part-to-Whole Ratios Converting Part-to-Part Ratios to Fractions, Decimals and Percents Converting Part-to-Whole Ratios to Fractions, Decimals and Percents Converting Various Fractions, Decimals, Percents and Part-to-Part Ratios Converting Various Fractions, Decimals, Percents and Part-to-Whole Ratios Converting Various Fractions, Decimals, Percents and Part-to-Part Ratios with 7ths and 11ths Converting Various Fractions, Decimals, Percents and Part-to-Whole Ratios with 7ths and 11ths
Adding and Subtracting Decimals
Try the following mental addition strategy for decimals. Begin by ignoring the decimals in the addition question. Add the numbers as if they were whole numbers. For example, 3.25 + 4.98 could be viewed as 325 + 498 = 823. Use an estimate to decide where to place the decimal. In the example, 3.25 + 4.98 is approximately 3 + 5 = 8, so the decimal in the sum must go between the 8 and the 2 (i.e. 8.23)
Adding Tenths Adding Decimal Tenths with 0 Before the Decimal (range 0.1 to 0.9) Adding Decimal Tenths with 1 Digit Before the Decimal (range 1.1 to 9.9) Adding Decimal Tenths with 2 Digits Before the Decimal (range 10.1 to 99.9)
Adding Hundredths Adding Decimal Hundredths with 0 Before the Decimal (range 0.01 to 0.99) Adding Decimal Hundredths with 1 Digit Before the Decimal (range 1.01 to 9.99) Adding Decimal Hundredths with 2 Digits Before the Decimal (range 10.01 to 99.99)
Adding Thousandths Adding Decimal Thousandths with 0 Before the Decimal (range 0.001 to 0.999) Adding Decimal Thousandths with 1 Digit Before the Decimal (range 1.001 to 9.999) Adding Decimal Thousandths with 2 Digits Before the Decimal (range 10.001 to 99.999)
Adding Ten Thousandths Adding Decimal Ten Thousandths with 0 Before the Decimal (range 0.0001 to 0.9999) Adding Decimal Ten Thousandths with 1 Digit Before the Decimal (range 1.0001 to 9.9999) Adding Decimal Ten Thousandths with 2 Digits Before the Decimal (range 10.0001 to 99.9999)
Adding Various Decimal Places Adding Various Decimal Places with 0 Before the Decimal Adding Various Decimal Places with 1 Digit Before the Decimal Adding Various Decimal Places with 2 Digits Before the Decimal Adding Various Decimal Places with Various Numbers of Digits Before the Decimal
European Format Adding Decimals European Format Adding decimal tenths with 0 before the decimal (range 0,1 to 0,9) European Format Adding decimal tenths with 1 digit before the decimal (range 1,1 to 9,9) European Format Adding decimal hundredths with 0 before the decimal (range 0,01 to 0,99) European Format Adding decimal hundredths with 1 digit before the decimal (range 1,01 to 9,99) European Format Adding decimal thousandths with 0 before the decimal (range 0,001 to 0,999) European Format Adding decimal thousandths with 1 digit before the decimal (range 1,001 to 9,999) European Format Adding decimal ten thousandths with 0 before the decimal (range 0,0001 to 0,9999) European Format Adding decimal ten thousandths with 1 digit before the decimal (range 1,0001 to 9,9999) European Format Adding mixed decimals with Various Decimal Places European Format Adding mixed decimals with Various Decimal Places (1 to 9 before decimal)
Base ten blocks can be used for decimal subtraction. Just redefine the blocks, so the big block is a one, the flat is a tenth, the rod is a hundredth and the little cube is a thousandth. Model and subtract decimals using base ten blocks, so students can "see" how decimals really work.
Subtracting Tenths Subtracting Decimal Tenths with No Integer Part Subtracting Decimal Tenths with an Integer Part in the Minuend Subtracting Decimal Tenths with an Integer Part in the Minuend and Subtrahend
Subtracting Hundredths Subtracting Decimal Hundredths with No Integer Part Subtracting Decimal Hundredths with an Integer Part in the Minuend and Subtrahend Subtracting Decimal Hundredths with a Larger Integer Part in the Minuend
Subtracting Thousandths Subtracting Decimal Thousandths with No Integer Part Subtracting Decimal Thousandths with an Integer Part in the Minuend and Subtrahend
Subtracting Ten Thousandths Subtracting Decimal Ten Thousandths with No Integer Part Subtracting Decimal Ten Thousandths with an Integer Part in the Minuend and Subtrahend
Subtracting Various Decimal Places Subtracting Various Decimals to Hundredths Subtracting Various Decimals to Thousandths Subtracting Various Decimals to Ten Thousandths
European Format Subtracting Decimals European Format Decimal subtraction (range 0,1 to 0,9) European Format Decimal subtraction (range 1,1 to 9,9) European Format Decimal subtraction (range 0,01 to 0,99) European Format Decimal subtraction (range 1,01 to 9,99) European Format Decimal subtraction (range 0,001 to 0,999) European Format Decimal subtraction (range 1,001 to 9,999) European Format Decimal subtraction (range 0,0001 to 0,9999) European Format Decimal subtraction (range 1,0001 to 9,9999) European Format Decimal subtraction with Various Decimal Places European Format Decimal subtraction with Various Decimal Places (1 to 9 before decimal)
Adding and subtracting decimals is fairly straightforward when all the decimals are lined up. With the questions arranged horizontally, students are challenged to understand place value as it relates to decimals. A wonderful strategy for placing the decimal is to use estimation. For example if the question is 49.2 + 20.1, the answer without the decimal is 693. Estimate by rounding 49.2 to 50 and 20.1 to 20. 50 + 20 = 70. The decimal in 693 must be placed between the 9 and the 3 as in 69.3 to make the number close to the estimate of 70.
The above strategy will go a long way in students understanding operations with decimals, but it is also important that they have a strong foundation in place value and a proficiency with efficient strategies to be completely successful with these questions. As with any math skill, it is not wise to present this to students until they have the necessary prerequisite skills and knowledge.
Horizontally Arranged Adding Decimals Adding Decimals to Tenths Horizontally Adding Decimals to Hundredths Horizontally Adding Decimals to Thousandths Horizontally Adding Decimals to Ten Thousandths Horizontally Adding Decimals Horizontally With Up to Two Places Before and After the Decimal Adding Decimals Horizontally With Up to Three Places Before and After the Decimal Adding Decimals Horizontally With Up to Four Places Before and After the Decimal
Horizontally Arranged Subtracting Decimals Subtracting Decimals to Tenths Horizontally Subtracting Decimals to Hundredths Horizontally Subtracting Decimals to Thousandths Horizontally Subtracting Decimals to Ten Thousandths Horizontally Subtracting Decimals Horizontally With Up to Two Places Before and After the Decimal Subtracting Decimals Horizontally With Up to Three Places Before and After the Decimal Subtracting Decimals Horizontally With Up to Four Places Before and After the Decimal
Horizontally Arranged Mixed Adding and Subtracting Decimals Adding and Subtracting Decimals to Tenths Horizontally Adding and Subtracting Decimals to Hundredths Horizontally Adding and Subtracting Decimals to Thousandths Horizontally Adding and Subtracting Decimals to Ten Thousandths Horizontally Adding and Subtracting Decimals Horizontally With Up to Two Places Before and After the Decimal Adding and Subtracting Decimals Horizontally With Up to Three Places Before and After the Decimal Adding and Subtracting Decimals Horizontally With Up to Four Places Before and After the Decimal
Multiplying and Dividing Decimals
Multiplying decimals by whole numbers is very much like multiplying whole numbers except there is a decimal to deal with. Although students might initially have trouble with it, through the power of rounding and estimating, they can generally get it quite quickly. Many teachers will tell students to ignore the decimal and multiply the numbers just like they would whole numbers. This is a good strategy to use. Figuring out where the decimal goes at the end can be accomplished by counting how many decimal places were in the original question and giving the answer that many decimal places. To better understand this method, students can round the two factors and multiply in their head to get an estimate then place the decimal based on their estimate. For example, multiplying 9.84 × 91, students could first round the numbers to 10 and 91 (keep 91 since multiplying by 10 is easy) then get an estimate of 910. Actually multiplying (ignoring the decimal) gets you 89544. To get that number close to 910, the decimal needs to go between the 5 and the 4, thus 895.44. Note that there are two decimal places in the factors and two decimal places in the answer, but estimating made it more understandable rather than just a method.
Multiplying Decimals by 1-Digit Whole Numbers Multiply 2-digit tenths by 1-digit whole numbers Multiply 2-digit hundredths by 1-digit whole numbers Multiply 2-digit thousandths by 1-digit whole numbers Multiply 3-digit tenths by 1-digit whole numbers Multiply 3-digit hundredths by 1-digit whole numbers Multiply 3-digit thousandths by 1-digit whole numbers Multiply various decimals by 1-digit whole numbers
Multiplying Decimals by 2-Digit Whole Numbers Multiplying 2-digit tenths by 2-digit whole numbers Multiplying 2-digit hundredths by 2-digit whole numbers Multiplying 3-digit tenths by 2-digit whole numbers Multiplying 3-digit hundredths by 2-digit whole numbers Multiplying 3-digit thousandths by 2-digit whole numbers Multiplying various decimals by 2-digit whole numbers
Multiplying Decimals by Tenths Multiplying 2-digit whole by 2-digit tenths Multiplying 2-digit tenths by 2-digit tenths Multiplying 2-digit hundredths by 2-digit tenths Multiplying 3-digit whole by 2-digit tenths Multiplying 3-digit tenths by 2-digit tenths Multiplying 3-digit hundredths by 2-digit tenths Multiplying 3-digit thousandths by 2-digit tenths Multiplying various decimals by 2-digit tenths
Multiplying Decimals by Hundredths Multiplying 2-digit whole by 2-digit hundredths Multiplying 2-digit tenths by 2-digit hundredths Multiplying 2-digit hundredths by 2-digit hundredths Multiplying 3-digit whole by 2-digit hundredths Multiplying 3-digit tenths by 2-digit hundredths Multiplying 3-digit hundredths by 2-digit hundredths Multiplying 3-digit thousandths by 2-digit hundredths Multiplying various decimals by 2-digit hundredths
Multiplying Decimals by Various Decimal Places Multiplying 2-digit by 2-digit numbers with various decimal places Multiplying 3-digit by 2-digit numbers with various decimal places
Decimal Long Multiplication in Various Ranges Decimal Multiplication (range 0.1 to 0.9) Decimal Multiplication (range 1.1 to 9.9) Decimal Multiplication (range 10.1 to 99.9) Decimal Multiplication (range 0.01 to 0.99) Decimal Multiplication (range 1.01 to 9.99) Decimal Multiplication (range 10.01 to 99.99) Random # Digits Random # Places
European Format Multiplying Decimals by 2-Digit Whole Numbers European Format 2-digit whole × 2-digit hundredths European Format 2-digit tenths × 2-digit whole European Format 2-digit hundredths × 2-digit whole European Format 3-digit tenths × 2-digit whole European Format 3-digit hundredths × 2-digit whole European Format 3-digit thousandths × 2-digit whole
European Format Multiplying Decimals by 2-Digit Tenths European Format 2-digit whole × 2-digit tenths European Format 2-digit tenths × 2-digit tenths European Format 2-digit hundredths × 2-digit tenths European Format 3-digit whole × 2-digit tenths European Format 3-digit tenths × 2-digit tenths European Format 3-digit hundredths × 2-digit tenths European Format 3-digit thousandths × 2-digit tenths
European Format Multiplying Decimals by 2-Digit Hundredths European Format 2-digit tenths × 2-digit hundredths European Format 2-digit hundredths × 2-digit hundredths European Format 3-digit whole × 2-digit hundredths European Format 3-digit tenths × 2-digit hundredths European Format 3-digit hundredths × 2-digit hundredths European Format 3-digit thousandths × 2-digit hundredths
European Format Multiplying Decimals by Various Decimal Places European Format 2-digit × 2-digit with various decimal places European Format 3-digit × 2-digit with various decimal places
Dividing Decimals by Whole Numbers Divide Tenths by a Whole Number Divide Hundredths by a Whole Number Divide Thousandths by a Whole Number Divide Ten Thousandths by a Whole Number Divide Various Decimals by a Whole Number
In case you aren't familiar with dividing with a decimal divisor, the general method for completing questions is by getting rid of the decimal in the divisor. This is done by multiplying the divisor and the dividend by the same amount, usually a power of ten such as 10, 100 or 1000. For example, if the division question is 5.32/5.6, you would multiply the divisor and dividend by 10 to get the equivalent division problem, 53.2/56. Completing this division will result in the exact same quotient as the original (try it on your calculator if you don't believe us). The main reason for completing decimal division in this way is to get the decimal in the correct location when using the U.S. long division algorithm.
A much simpler strategy, in our opinion, is to initially ignore the decimals all together and use estimation to place the decimal in the quotient. In the same example as above, you would complete 532/56 = 95. If you "flexibly" round the original, you will get about 5/5 which is about 1, so the decimal in 95 must be placed to make 95 close to 1. In this case, you would place it just before the 9 to get 0.95. Combining this strategy with the one above can also help a great deal with more difficult questions. For example, 4.584184 ÷ 0.461 can first be converted the to equivalent: 4584.184 ÷ 461 (you can estimate the quotient to be around 10). Complete the division question without decimals: 4584184 ÷ 461 = 9944 then place the decimal, so that 9944 is about 10. This results in 9.944.
Dividing decimal numbers doesn't have to be too difficult, especially with the worksheets below where the decimals work out nicely. To make these worksheets, we randomly generated a divisor and a quotient first, then multiplied them together to get the dividend. Of course, you will see the quotients only on the answer page, but generating questions in this way makes every decimal division problem work out nicely.
Decimal Long Division with Quotients That Work Out Nicely Dividing Decimals by Various Decimals with Various Sizes of Quotients Dividing Decimals by 1-Digit Tenths (e.g. 0.72 ÷ 0.8 = 0.9) Dividing Decimals by 1-Digit Tenths with Larger Quotients (e.g. 3.2 ÷ 0.5 = 6.4) Dividing Decimals by 2-Digit Tenths (e.g. 10.75 ÷ 2.5 = 4.3) Dividing Decimals by 2-Digit Tenths with Larger Quotients (e.g. 387.75 ÷ 4.7 = 82.5) Dividing Decimals by 3-Digit Tenths (e.g. 1349.46 ÷ 23.8 = 56.7) Dividing Decimals by 2-Digit Hundredths (e.g. 0.4368 ÷ 0.56 = 0.78) Dividing Decimals by 2-Digit Hundredths with Larger Quotients (e.g. 1.7277 ÷ 0.39 = 4.43) Dividing Decimals by 3-Digit Hundredths (e.g. 31.4863 ÷ 4.61 = 6.83) Dividing Decimals by 4-Digit Hundredths (e.g. 7628.1285 ÷ 99.91 = 76.35) Dividing Decimals by 3-Digit Thousandths (e.g. 0.076504 ÷ 0.292 = 0.262) Dividing Decimals by 3-Digit Thousandths with Larger Quotients (e.g. 2.875669 ÷ 0.551 = 5.219)
These worksheets would probably be used for estimating and calculator work.
Horizontally Arranged Decimal Division Random # Digits Random # Places
European Format Dividing Decimals with Quotients That Work Out Nicely European Format Divide Tenths by a Whole Number European Format Divide Hundredths by a Whole Number European Format Divide Thousandths by a Whole Number European Format Divide Ten Thousandths by a Whole Number European Format Divide Various Decimals by a Whole Number
In the next set of questions, the quotient does not always work out well and may have repeating decimals. The answer key shows a rounded quotient in these cases.
European Format Dividing Decimals by Whole Numbers European Format Divide Tenths by a Whole Number European Format Divide Hundredths by a Whole Number European Format Divide Thousandths by a Whole Number European Format Divide Ten Thousandths by a Whole Number European Format Divide Various Decimals by a Whole Number
European Format Dividing Decimals by Decimals European Format Decimal Tenth (0,1 to 9,9) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Hundredth (0,01 to 9,99) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Thousandth (0,001 to 9,999) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Ten Thousandth (0,0001 to 9,9999) Divided by Decimal Tenth (1,1 to 9,9) European Format Various Decimal Places (0,1 to 9,9999) Divided by Decimal Tenth (1,1 to 9,9) European Format Various Decimal Places (0,1 to 9,9999) Divided by Various Decimal Places (1,1 to 9,9999)
"Could I have a 3.65 and an 0.8, please ... ?" NO, not THAT type of ordering. I mean putting them in order ...
Ordering decimals can be tricky. Because often we look at 0.42 and 0.402 and say that 0.402 must be bigger because there are more digits. But no!
We can use this method to see which decimals are bigger:
Set up a table with the decimal point in the same place for each number.
Put in each number.
Fill in the empty squares with zeros .
Compare using the first column on the left
If the digits are equal move to the next column to the right until one number wins.
For order we pick the smallest first
For order we pick the largest first
Example: Put the following decimals in ascending order:
1.506, 1.56, 0.8
In a table they look like this:
Ones
Decimal Point
Tenths
Hundredths
Thousandths
1
.
5
0
6
1
.
5
6
0
.
8
Fill in the empty squares with zeros:
Ones
Decimal Point
Tenths
Hundredths
Thousandths
1
.
5
0
6
1
.
5
6
0
0
.
8
0
0
Compare using the first column (Ones)
Two of them are "1"s and the other is a "0". Ascending order needs smallest first, and so "0" is the winner:
Answer so far: 0.8
Now we can remove 0.8 from the list:
Ones
Decimal Point
Tenths
Hundredths
Thousandths
1
.
5
0
6
1
.
5
6
0
-
.
-
-
-
Compare the Tenths
Now there are two numbers with the same "Tenths" value of 5, so move along to the "Hundredths" for the tie-breaker
Compare the Hundredths
One of those has a 6 in the hundredths, and the other has a 0, so the 0 wins (remember we are looking for the smallest each time). In other words 1.506 is less than 1.56:
Answer so far: 0.8, 1.506
Remove 1.506 from the list:
Ones
Decimal Point
Tenths
Hundredths
Thousandths
-
.
-
-
-
1
.
5
6
0
-
.
-
-
-
Only one number left, it must be the largest:
Answer: 0.8, 1.506, 1.56
Example: Put the following decimals in DESCENDING order:
0.402, 0.42, 0.375, 1.2, 0.85
Ones
Decimal Point
Tenths
Hundredths
Thousandths
0
.
4
0
2
0
.
4
2
0
.
3
7
5
1
.
2
0
.
8
5
And we want to go from highest to lowest (descending).
Ones
Decimal Point
Tenths
Hundredths
Thousandths
0
.
4
0
2
0
.
4
2
0
0
.
3
7
5
1
.
2
0
0
0
.
8
5
0
Compare using the first column (Ones):
There is a 1, all the rest are 0. Descending order needs largest first, so 1.2 must be the highest. (Write it down in your answer and cross it off the table).
Answer so far: 1.2
Ones
Decimal Point
Tenths
Hundredths
Thousandths
0
.
4
0
2
0
.
4
2
0
0
.
3
7
5
-
-
-
-
-
0
.
8
5
0
Compare the Tenths.
The 8 is highest, so 0.85 is next in value.
Answer so far: 1.2, 0.85
Ones
Decimal Point
Tenths
Hundredths
Thousandths
0
.
4
0
2
0
.
4
2
0
0
.
3
7
5
-
-
-
-
-
-
-
-
-
-
Now there are two numbers with the same "Tenths" value of 4, so move along to the "Hundredths" for the tie-breaker
One number has a 2 in the hundredths, and the other has a 0, so the 2 wins. So 0.42 is bigger than 0.402:
Answer so far: 1.2, 0.85, 0.42, 0.402
Ones
Decimal Point
Tenths
Hundredths
Thousandths
-
-
-
-
-
-
-
-
-
-
0
.
3
7
5
-
-
-
-
-
-
-
-
-
-
Only 0.375 left, so the answer is:
Answer: 1.2, 0.85, 0.42, 0.402, 0.375
Now, go practice with this special Decimal Ordering Game !
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Click here for Answers. . Practice Questions. Previous: Multiplying/Dividing by Decimals Practice Questions. Next: Dimensional Analysis Practice Questions. The Corbettmaths Practice Questions on Ordering Decimals.
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Step 1: Step 2: The least decimal is 9.75. Now we must determine how 9.75 compares with the winning score. Answer: The last swimmer must get a score less than 9.75 s in order to win. Example 4: To make a miniature ice cream truck, you need tires with a diameter between 1.465 cm and 1.472 cm.
Step 1: Use the place value chart! Write the decimals in the place value chart such that the place values of all the decimals are aligned. The empty boxes at the end of the decimal can be filled with zeroes. Step 2: Compare the whole number part first. Always start comparing the digits at the highest place value.
Decimals Worksheets
These decimals worksheets will produce decimal multiplication problems with facts being powers of ten. It may be configured for 1, 2, or 3 digits on the right of the decimal and up to 2 digits on the left. You may vary the numbers of problems on each worksheet from 12 to 25. Ordering Decimal Numbers Worksheets.
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Ordering Decimals up to 3dp. Here you will find a range of free printable math worksheets, which will help your child learn to order numbers with up to 3 decimal places. Using these sheets will help your child to: learn to order numbers with 1, 2, or 3 decimal places; learn to order positive and negative decimals.
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There are seven problems in each pdf worksheet for grade 4 and grade 5. Download the set. Ordering Decimals - Standard | Level 2. Levitate your ordering practice with these worksheets featuring decimals with up to thousandths places. Write the decimals in the ascending order in part A and the descending order in part B.
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Here's an example: Order the following decimals in ascending order: 0.25, 0.5, 0.17, 0.45, 0.23. Compare whole number parts: All whole number parts are 0, so move to the decimal parts. Compare decimal parts: Order the numbers according to the digits in the tenths place. If there are any numbers with the same digit in the tenths place then ...
Ordering Decimals
Ordering Decimals - Grid Puzzles. A Bronze/Silver/Gold differentiated resource where pupils are given a list of decimals and a square grid. Pupils have to put the decimals into the grid so that each row and column is in ascending order. In Bronze, the integer part of each decimal is the same. In Silver, the integer parts are different.
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This Decimals Worksheet will produce problems that involve ordering decimal numbers. The student will be given a list of decimal numbers and be asked to order them in ascending or descending order. You may select the number of problems per worksheets, the number of decimal numbers to sort per problem, the number of digits in each decimal number, as well as the way to order the decimal numbers.
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Order Decimal Numbers — Online Practice Game (grades 4-7) Practice ordering decimals (from the smallest to the greatest) by dragging them into "boxes" in the correct order. You can choose to order either 3 or 4 decimals. You can also choose the number of decimal digits for the numbers. For example, students in 4th grade might use decimals ...
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In the examples above, the decimals in each problem had the same number of digits. Thus, they lined up nicely, one beneath the other. Let's look at some examples in which the decimals presented have a different number of decimal digits. Example 3: Order these decimals from least to greatest: 6.01, 0.601, 6.1
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Ordering decimals
Ordering decimals. Author: Jess Prior. This type of activity is known as Practice. Please read the guidance notes here, where you will find useful information for running these types of activities with your students. 1. Example-Problem Pair. 2. Intelligent Practice. 3.
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Examples, solutions, videos, worksheets, stories, and songs to help Grade 5 students learn how to compare and order decimals. This is a short video tutorial on comparing and arranging decimals. Decimals Comparing and Ordering. A song on how to use the > and < symbols. eats the value that is greater.
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Follow us. Improve your math knowledge with free questions in "Compare, order, and round decimals: word problems" and thousands of other math skills.
To write decimals from least to greatest and vice versa, we need to first compare the decimals two at a time. Example: Order the decimals. 1.243, 0.243, and 1.24. Solution: Step 1: Compare the decimals two at a time. 1.243 > 1.24. 1.24 > 0.243. Step 2: List the decimals from least to greatest. 0.243, 1.24, 1.243
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Decimals word problems. Welcome to our page for problems with decimal numbers! Here you will find interactive practice and printable worksheets to practice solving word problems involving decimal numbers, such as problems with money, problems with real-life data, and other problems and challenges which include decimal numbers.
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Thanks for visiting the Decimals Worksheets page at Math-Drills.Com where we make a POINT of helping students learn. On this page, you will find Decimals worksheets on a variety of topics including comparing and sorting decimals, adding, subtracting, multiplying and dividing decimals, and converting decimals to other number formats. To start, you will find the general use printables to be ...
PDF All Decimal Operations with Word Problems
All Decimal Operations with Word Problems. 1) Ellen wanted to buy the following items: A DVD player for $49.95. A DVD holder for $19.95. Personal stereo for $21.95. Does Ellen have enough money to buy all three items if she has $90. 2) Melissa purchased $39.46 in groceries at a store.
Ordering Decimals
Ordering decimals can be tricky. Because often we look at 0.42 and 0.402 and say that 0.402 must be bigger because there are more digits. But no! We can use this method to see which decimals are bigger: Set up a table with the decimal point in the same place for each number. Put in each number. Fill in the empty squares with zeros.
White Rose Maths Compatible Ordering Decimals Year 4 Mastery
In this set of numbers, 2.7 would come first. Next, there are two numbers with the same ones digit (3.5 and 3.8) so we look at the tenths digit and see that 5 tenths is less than 8 tenths so 3.5 comes next. These numbers in ascending number are: 2.7, 3.5, 3.8, 4.7. With these steps, you can easily teach ordering decimals to year 4 students!
Ordering Decimals Word Problems Teaching Resources
4.9. (15) $3.00. PDF. This resource is includes practice pages for comparing and ordering decimals as well as real world word problems that require application of the skills. Includes: ~ 2 pages comparing decimals ~ 2 pages ordering decimals ~ 4 pages word problems ( mixed compare and order) This is part of my Comparing Decimals Bundle This ...
IMAGES
VIDEO
COMMENTS
Click here for Answers. . Practice Questions. Previous: Multiplying/Dividing by Decimals Practice Questions. Next: Dimensional Analysis Practice Questions. The Corbettmaths Practice Questions on Ordering Decimals.
Step 1: Step 2: The least decimal is 9.75. Now we must determine how 9.75 compares with the winning score. Answer: The last swimmer must get a score less than 9.75 s in order to win. Example 4: To make a miniature ice cream truck, you need tires with a diameter between 1.465 cm and 1.472 cm.
Step 1: Use the place value chart! Write the decimals in the place value chart such that the place values of all the decimals are aligned. The empty boxes at the end of the decimal can be filled with zeroes. Step 2: Compare the whole number part first. Always start comparing the digits at the highest place value.
These decimals worksheets will produce decimal multiplication problems with facts being powers of ten. It may be configured for 1, 2, or 3 digits on the right of the decimal and up to 2 digits on the left. You may vary the numbers of problems on each worksheet from 12 to 25. Ordering Decimal Numbers Worksheets.
Ordering Decimals up to 3dp. Here you will find a range of free printable math worksheets, which will help your child learn to order numbers with up to 3 decimal places. Using these sheets will help your child to: learn to order numbers with 1, 2, or 3 decimal places; learn to order positive and negative decimals.
There are seven problems in each pdf worksheet for grade 4 and grade 5. Download the set. Ordering Decimals - Standard | Level 2. Levitate your ordering practice with these worksheets featuring decimals with up to thousandths places. Write the decimals in the ascending order in part A and the descending order in part B.
Here's an example: Order the following decimals in ascending order: 0.25, 0.5, 0.17, 0.45, 0.23. Compare whole number parts: All whole number parts are 0, so move to the decimal parts. Compare decimal parts: Order the numbers according to the digits in the tenths place. If there are any numbers with the same digit in the tenths place then ...
Ordering Decimals - Grid Puzzles. A Bronze/Silver/Gold differentiated resource where pupils are given a list of decimals and a square grid. Pupils have to put the decimals into the grid so that each row and column is in ascending order. In Bronze, the integer part of each decimal is the same. In Silver, the integer parts are different.
This Decimals Worksheet will produce problems that involve ordering decimal numbers. The student will be given a list of decimal numbers and be asked to order them in ascending or descending order. You may select the number of problems per worksheets, the number of decimal numbers to sort per problem, the number of digits in each decimal number, as well as the way to order the decimal numbers.
Order Decimal Numbers — Online Practice Game (grades 4-7) Practice ordering decimals (from the smallest to the greatest) by dragging them into "boxes" in the correct order. You can choose to order either 3 or 4 decimals. You can also choose the number of decimal digits for the numbers. For example, students in 4th grade might use decimals ...
In the examples above, the decimals in each problem had the same number of digits. Thus, they lined up nicely, one beneath the other. Let's look at some examples in which the decimals presented have a different number of decimal digits. Example 3: Order these decimals from least to greatest: 6.01, 0.601, 6.1
Decimal Word Problems Worksheets: 1-Step Word Problems, Add, Subtract. 2-Step Word Problems, Add, Subtract. Decimal Word Problems (Mixed Op) Decimal Word Problems (Mixed Op) Objective: I can solve word problems involving addition, subtraction, multiplication and division of decimals. Share this page to Google Classroom.
Ordering decimals. Author: Jess Prior. This type of activity is known as Practice. Please read the guidance notes here, where you will find useful information for running these types of activities with your students. 1. Example-Problem Pair. 2. Intelligent Practice. 3.
Examples, solutions, videos, worksheets, stories, and songs to help Grade 5 students learn how to compare and order decimals. This is a short video tutorial on comparing and arranging decimals. Decimals Comparing and Ordering. A song on how to use the > and < symbols. eats the value that is greater.
Follow us. Improve your math knowledge with free questions in "Compare, order, and round decimals: word problems" and thousands of other math skills.
To write decimals from least to greatest and vice versa, we need to first compare the decimals two at a time. Example: Order the decimals. 1.243, 0.243, and 1.24. Solution: Step 1: Compare the decimals two at a time. 1.243 > 1.24. 1.24 > 0.243. Step 2: List the decimals from least to greatest. 0.243, 1.24, 1.243
Decimals word problems. Welcome to our page for problems with decimal numbers! Here you will find interactive practice and printable worksheets to practice solving word problems involving decimal numbers, such as problems with money, problems with real-life data, and other problems and challenges which include decimal numbers.
Decimal Place Value Worksheets. Here you will find our selection of Place Value involving Decimals with up to 2 decimal places (2dp). Using these sheets will help your child learn to: learn their place value with decimals up to 3dp; understand the value of each digit in a decimal number; learn to read and write numbers with up to 3dp.
Thanks for visiting the Decimals Worksheets page at Math-Drills.Com where we make a POINT of helping students learn. On this page, you will find Decimals worksheets on a variety of topics including comparing and sorting decimals, adding, subtracting, multiplying and dividing decimals, and converting decimals to other number formats. To start, you will find the general use printables to be ...
All Decimal Operations with Word Problems. 1) Ellen wanted to buy the following items: A DVD player for $49.95. A DVD holder for $19.95. Personal stereo for $21.95. Does Ellen have enough money to buy all three items if she has $90. 2) Melissa purchased $39.46 in groceries at a store.
Ordering decimals can be tricky. Because often we look at 0.42 and 0.402 and say that 0.402 must be bigger because there are more digits. But no! We can use this method to see which decimals are bigger: Set up a table with the decimal point in the same place for each number. Put in each number. Fill in the empty squares with zeros.
In this set of numbers, 2.7 would come first. Next, there are two numbers with the same ones digit (3.5 and 3.8) so we look at the tenths digit and see that 5 tenths is less than 8 tenths so 3.5 comes next. These numbers in ascending number are: 2.7, 3.5, 3.8, 4.7. With these steps, you can easily teach ordering decimals to year 4 students!
4.9. (15) $3.00. PDF. This resource is includes practice pages for comparing and ordering decimals as well as real world word problems that require application of the skills. Includes: ~ 2 pages comparing decimals ~ 2 pages ordering decimals ~ 4 pages word problems ( mixed compare and order) This is part of my Comparing Decimals Bundle This ...