percentage error homework

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Percentage Error

Percentage error is a measurement of the discrepancy between an observed (measured) and a true (expected, accepted, known etc.) value. It is typically used to compare measured vs. known values as well as to assess whether the measurements taken are valid.

When measuring data, whether it be the density of some material, standard acceleration due to gravity of a falling object, or something else entirely, the measured value often varies from the true value. Error can arise due to many different reasons that are often related to human error, but can also be due to estimations and limitations of devices used in measurement. Calculating the percentage error provides a means to quantify the degree by which a measured value varies relative to the true value. A small percentage error means that the observed and true value are close while a large percentage error indicates that the observed and true value vary greatly. In most cases, a small percentage error is desirable, while a large percentage error may indicate an error or that an experiment or measurement technique may need to be re-evaluated. If, for example, the measured value varies from the expected value by 90%, there is likely an error, or the method of measurement may not be accurate.

Computing percentage error

The computation of percentage error involves the use of the absolute error, which is simply the difference between the observed and the true value. The absolute error is then divided by the true value, resulting in the relative error, which is multiplied by 100 to obtain the percentage error. Refer to the equations below for clarification.

For example, if the observed value is 56.891 and the true value is 62.327, the percentage error is:

The equations above are based on the assumption that true values are known. True values are often unknown, and under these situations, standard deviation is one way to represent the error. Please refer to the standard deviation calculator for further details.

Negative percentage error

Based on the formula above, when the true value is positive, percentage error is always positive due to the absolute value. In most cases, only the error is important, and not the direction of the error. However, it is possible to have a negative percentage error. This occurs if we do not take the absolute value of the error, the observed value is smaller than the true value, and the true value is positive. For example, given an observed value of 7, a true value of 9, and allowing for a negative percentage, the percentage error is:

A negative percentage error simply means that the observed value is smaller than the true value. If the observed value is larger than the true value, the percentage error will be positive. Thus, in the context of an experiment, a negative percentage error just means that the measured value is smaller than expected. It does not indicate that the observed value is somehow better than expected, since the best possible outcome for percentage error is that the observed and true values are equal, resulting in a percentage error of 0.

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Percent Error

Percent errors indicate how big our errors are when we measure something in an analysis process. Smaller percent errors indicate that we are close to the accepted or original value. For example, a 1% error indicates that we got very close to the accepted value, while 48% means that we were quite a long way off from the true value. Measurement errors are often unavoidable due to certain reasons like hands can shake, material can be imprecise, or our instruments just might not have the capability to estimate exactly. Percent error formula will let us know how seriously these inevitable errors influenced our results.

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

Percent Error Formula

The formula for percent error is:

PE = (|Estimated value-Actual value|/ Actual value) × 100

T = True or Actual value

E = Estimated value

How is the percent error calculated?

Below steps describe how to obtain the percent error in detail.

Step 1:Take the difference of one value from another. If we are ignoring the sign, the order does not matter. But we need to subtract the original value from the determined value if we are keeping negative signs. This value is “error.”

Step 2: Perform division operation for the error by the accurate or ideal value (not estimated or measured value). This results in a decimal number.

Step 3: Multiply it by 100 to transform a decimal number into a percentage.

Step 4: Add a percentage symbol (%) to represent percent error value.

Percent Error of Mean

Percent error mean or Mean percentage error is the average of all percent errors of the given model. The formula for mean percentage error is given by:

T i = True or actual value of i th quantity

E i = Estimated value of i th quantity

n = number of quantities in the model

The main disadvantage of this measure is that it is undefined, whenever a single actual value is zero.

How To Calculate Percentage

Percentage Increase Decrease

Percent Error Example

The below examples help in better understanding of percent error.

A boy measured the area of a rectangle plot to be 468 cm 2 . But the actual area of the plot has been recorded as 470 cm 2 . Calculate the percent error of his measurement.

Measured area value = 468 cm 2

Actual area value = 470 cm 2

Steps of calculation:

Step 1: Subtract one value from another; 468 – 470 = -2

By ignoring the negative sign, the difference is 2, which is the error.

Step 2: Divide the error by actual value; 2/470 = 0.0042531

Multiply this value by 100; 0.0042531 × 100 = 0.42% (expressing it in two decimal points) Hence, 0.42% is the percent error.

A person started a new business on 1st January. Based on the demand in that particular area, he expected a certain number of customers who can visit his shop per month. The following table gives the information on the number of visitors for the shop during the first quarter.

Find the mean percent error for the above data.

Mean percent error = (11.11% + 20% + 5%)/ 3

=12.0367% (approx)

The purpose of calculating the percent error is to analyse how close the measured value is to an actual value. It is part of a comprehensive error analysis. In most of the fields, percent error is always expressed as a positive number whereas in others, it is correct to have either a positive or negative value. The idea of keeping the sign is to determine whether recorded values consistently fall above or below expected values.

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Calculate Percent Error 5

Percent Error Definition

Percent error, sometimes referred to as percentage error, is an expression of the difference between a measured value and the known or accepted value . It is often used in science to report the difference between experimental values and expected values.

The formula for calculating percent error is:

Note: occasionally, it is useful to know if the error is positive or negative. If you need to know the positive or negative error, this is done by dropping the absolute value brackets in the formula. In most cases, absolute error is fine. For example, in experiments involving yields in chemical reactions, it is unlikely you will obtain more product than theoretically possible.

Steps to Calculate the Percent Error

• Subtract the accepted value from the experimental value.
• Take the absolute value of step 1
• Divide that answer by the accepted value.
• Multiply that answer by 100 and add the % symbol to express the answer as a percentage .

Example Calculation

Now let’s try an example problem.

You are given a cube of pure copper. You measure the sides of the cube to find the volume and weigh it to find its mass. When you calculate the density using your measurements, you get 8.78 grams/cm 3 . Copper’s accepted density is 8.96 g/cm 3 . What is your percent error?

Solution: experimental value = 8.78 g/cm 3 accepted value = 8.96 g/cm 3

Step 1: Subtract the accepted value from the experimental value.

8.78 g/cm 3 – 8.96 g/cm 3 = -0.18 g/cm 3

Step 2: Take the absolute value of step 1

|-0.18 g/cm 3 | = 0.18 g/cm 3

Step 3: Divide that answer by the accepted value.

Step 4: Multiply that answer by 100 and add the % symbol to express the answer as a percentage.

0.02 x 100 = 2 2%

The percent error of your density calculation is 2%.

Related Posts

5 thoughts on “ calculate percent error ”.

Percent error is always represented as a positive value. The difference between the actual and experimental value is always the absolute value of the difference. |Experimental-Actual|/Actualx100 so it doesn’t matter how you subtract. The result of the difference is positive and therefore the percent error is positive.

Percent error is always positive, but step one still contains the error initially flagged by Mark. The answer in that step should be negative:

experimental-accepted=error 8.78 – 8.96 = -0.18

In the article, the answer was edited to be correct (negative), but the values on the left are still not in the right order and don’t yield a negative answer as presented.

Mark is not correct. Percent error is always positive regardless of the values of the experimental and actual values. Please see my post to him.

Say if you wanted to find acceleration caused by gravity, the accepted value would be the acceleration caused by gravity on earth (9.81…), and the experimental value would be what you calculated gravity as 🙂

If you don’t have an accepted value, the way you express error depends on how you are making the measurement. If it’s a calculated value, like, based on a known about of carbon dioxide dissolved in water, then you have a theoretical value to use instead of the accepted value. If you are performing a chemical reaction to quantify the amount of carbonic acid, the accepted value is the theoretical value if the reaction goes to completion. If you are measuring the value using an instrument, you have uncertainty of the instrument (e.g., a pH meter that measures to the nearest 0.1 units). But, if you are taking measurements, most of the time, measure the concentration more than once, take the average value of your measurements, and use the average (mean) as your accepted value. Error gets complicated, since it also depends on instrument calibration and other factors.

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How to Calculate the Percentage Error (Pictures and Examples)

Video lesson: calculating percentage error, the percentage error formula.

• Percentage Error = |[(Measured Value – True Value) / True Value]| x 100
• Where the Measured Value is the value obtained through measurement or observation.
• Where the True Value is the actual, theoretical or accepted value of the quantity being measured.
• The absolute value is used to ensure that the error is always positive.

Formula for calculating the percentage error

The absolute value “| |” is used to ensure that the percentage error calculated is postive.

So if the result of this part of the formula is negative, it becomes positive and if it is already positive, it remains as positive.

This calculation tells us the absolute error.

For example: My height is measured as 182 cm but my actual height is 174 cm. Find the percentage error in the measurement.

• The measured value is 182 cm
• The true value is 174 cm

The percent error in the height measurement is 4.60%.

For example: I measure 33 g of a substance but there is actually 40 g. Find the percentage error in the measurement.

In this example the measured value is lower than the true value and so, the absolute value operation “| |” will be used to make the answer positive.

• The measured value is 33 g.
• The true value is 40 g.

Steps to Find the Percent Error

The percent error formula can be broken down into three simple steps based on the order of the calculations.

Following these steps will find the same result as using the percentage error formula but some people may prefer this method.

• Find the difference between the true value and the measured value.
• Divide this result by the true value.
• Multiply this result by 100.

For example: I measure 26 mL of liquid but the true amount there is 21 mL. Find the percentage error in measurement.

Step 1. Find the difference between the true value and the measured value

• The measured value is 26
• The true value is 21

The difference between the values is found by subtracting the smaller value from the larger value.

26 – 21 = 5 and so, the difference between the measured and true value is 5.

Step 2. Divide this result by the true value

The true value is 21 and so we divide 5 by 21.

5 ÷ 21 ≈ 0.238.

Step 3. Multiply this result by 100

0.238 × 100 = 23.8

Therefore the percentage error is 23.8%.

Percentage errors are often measured to 3 significant figures and can take decimal values.

What is Percentage Error and Why is it Important?

Percentage error is the difference between a measurement and its actual value. This difference is expressed as a percentage of the actual value. It is used in scientific experiments to compare an experimental value to the expected or known value.

• The percentage error is simply given as a percentage without any units.
• The larger the percentage error, the greater the inaccuracy in the experiment or measurement.
• A smaller percentage error indicates a greater level of precision and accuracy.

Percentage error is a measure of how different an experimental result is from the expected or true value. This is important in scientific experiments where small errors can be very significant.

• Percentage error can be used to determine the accuracy and reliability of results.
• Measuring percentage error can be useful as adjustments can be made to the experimental methods to reduce the error of future experiments.
• Percentage error can be used to identify apparatus malfunction or imprecision of equipment.
• Percentage error can be used in manufacturing processes to identify sources of errors so that a better product can be made.
• Percentage error can be used to improve the quality and efficiency of manufacturing processes and reduce waste.

Percentage error is also known as relative error. This is because the difference between the measured and true values is always compared relative to the true value.

What is an Acceptable Percentage Error?

The acceptable level of percentage error depends on the level of accuracy required for the experiment and the precision of the measuring instruments involved. Many scientific experiments may allow a 1% error as a result of imprecision in the instruments however in high-precision, medical or safety experiments the acceptable error may be 0.1% or lower.

As a rule, large percentage error is not good and reducing the percentage error present is always positive.

In situations where a certain degree of variability is expected, a higher percentage error may be acceptable. For example, a percentage error of 5% may be acceptable in public opinion polls.

It is possible to have 0% percentage error. This occurs when the measured value is identical to the true value and there is no difference or error present).

Percentage Error over 100%

A percentage error of 100% means that the measured result is double the true value. Therefore it is a significantly large error. Percentage errors larger than 100% can occur and they mean that the measured result is more than double the true value.

For example:

• A percentage error of 100% means the measured value is double the true value
• A percentage error of 200% means the measured value is triple the true value
• A percentage error of 300% means the measured value is quadruple the true value
• A percentage error of 400% means the measured value is five times the true value

While a percentage error over 100% may seem extreme, it can still be useful to calculate and report it as it still provides information on the magnitude of the error. However, it is important to consider the context of the measurement or calculation and the potential sources of error that may have contributed to such a large percentage error.

In general, a percentage error over 100% suggests that there may be significant issues with the measurement or calculation, and further investigation and re-evaluation may be necessary to ensure accuracy.

Negative Percentage Error

In the percentage error formula, the absolute value operation ensures that all percentage errors are given as a positive value. However, it can be useful to calculate negative percentage errors which tell us tha t the measured value is less than the true value. If negative percentage errors are desired, do not take the absolute value in the percentage error calculation.

The percentage error formula including negative percentage errors

• Positive percentage error means that the measured result is larger than the true value
• Negative percentage error means that the measured result is less than the true value

For example, we can see that compared to the true value of 50, the measured values below that are above 50 have a positive percentage error and the measured values below 50 have a negative percentage error.

While negative percentage errors can be less common than positive percentage errors, they are still important to report as they provide valuable information on the accuracy of the measurement or calculation.

Negative percentage errors help indicate how many results are above or below the expected value and as such, they can be used to improve the accuracy of an experiment.

Examples of Calculating Percentage Error

Here are some examples of calculating the percentage error.

Percentage Error for Multiple Trials

To find the percentage error for multiple trials of an experiment, calculate the average of these values and use this average in place of the measured value in the percent error formula.

The formula then becomes:

Formula for the Percentage Error for Multiple Trials

• Calculate the average of the measured values by adding them all together and dividing by the number of trials.
• Calculate the difference between the average measured value and the actual value using absolute value.
• Divide this difference by the actual value.
• Multiply the result by 100 to convert it to a percentage.

For example, 5 trials were conducted to determine the mass of an object which obtained the following results: 10.2 g, 10.1 g, 10.3 g, 10.0 g, and 10.2 g.

The mass of the object is known to be 10.5 g.

Find the percentage error for these 5 trials.

• Calculate the average measured value:

Average measured value = (10.2 + 10.1 + 10.3 + 10.0 + 10.2) / 5 = 10.16 g

• Calculate the difference between the average measured value and the actual value using absolute value:

Percent error = [(|10.16 – 10.5|) / 10.5] x 100%

Percent error = [0.34 / 10.5] x 100%

Percent error = 3.24%

Therefore, the percent error for these 5 trials is 3.24%.

How to Calculate the Percentage Error in Excel

To find the percentage error using Excel, use the following formula:

=ABS((Measured Value - True Value) / True Value) * 100

To use this formula:

• Enter the measured value in one cell, say A2.
• Enter the true value in another cell, say B2.
• Enter the above formula in a cell and replace “Measured Value” with the cell reference of the measured value (A2) and “True Value” with the cell reference of the true value (B2).

With a measured value in cell A2 and a true value in cell B2, the excel formula to find the percentage error becomes:

=ABS((A2-B2)/B2)*100

Note that the ABS function is used to get the absolute value of the difference between the actual and estimated value. Multiplying the result by 100 converts the value to a percentage.

For example in the cells above, the measured value of 34 is in cell A2 and the true value of 30 is in cell B2.

In cell C2 we type “=ABS((A2-B2)/B2)*100 and press enter.

The result of 13.3% error is obtained.

Illustrative Mathematics Grade 7, Unit 4, Lesson 14: Percent Error

Learning Targets:

• I can solve problems that involve percent error.

Related Pages Illustrative Math Grade 7

Lesson 14: Percent Error

Let’s use percentages to describe other situations that involve error.

Illustrative Math Unit 7.4, Lesson 14 (printable worksheets)

Lesson 14 Summary

Percent error can be used to describe any situation where there is a correct value and an incorrect value, and we want to describe the relative difference between them. For example, if a milk carton is supposed to contain 16 fluid ounces and it only contains 15 fluid ounces:

• the measurement error is 1 oz, and
• the percent error is 6.25% because 1 ÷ 16 = 0.0625. We can also use percent error when talking about estimates. For example, a teacher estimates there are about 600 students at their school. If there are actually 625 students, then the percent error for this estimate was 4%, because 625 - 600 = 15 and 35 ÷ 625 = 0.04

Lesson 14.1 Number Talk: Estimating a Percentage of a Number

Estimate. 25% of 15.8 9% of 38 1.2% of 127 0.53% of 6 0.06% of 202

Lesson 14.2 Plants, Bicycles, and Crowds

• Instructions to care for a plant say to water it with 3/4 cup of water every day. The plant has been getting 25% too much water. How much water has the plant been getting?
• The pressure on a bicycle tire is 63 psi. This is 5% higher than what the manual says is the correct pressure. What is the correct pressure?
• The crowd at a sporting event is estimated to be 2,500 people. The exact attendance is 2,486 people. What is the percent error?

Are you ready for more?

A micrometer is an instrument that can measure lengths to the nearest micron (a micron is a millionth of a meter). Would this instrument be useful for measuring any of the following things? If so, what would the largest percent error be?

Since it is measured to the nearest micron. The greatest possible error is 0.5 micron. (see Greatest Possible Error ) The greatest percent error = 0.5 micron ÷ 0.1 millimeters · 100% = 0.5 micron ÷ 100 microns · 100% = 0.5% The micrometer is useful for measuring an eyelash because the greatest percent error is only 0.5%

The greatest percent error = 0.5 micron ÷ 8 microns · 100% = 6.25% The micrometer is not very suitable for measuring a red blood cell because the greatest percent error is 6.25%

The greatest percent error = 0.5 micron ÷ 100 picometers · 100% = 0.5 micron ÷ 0.0001 microns · 100% = 500,000% The micrometer is definitely not suitable for measuring the diameter of a hydrogen atom because the greatest percent error is 500,000%

Lesson 14.3 Measuring in the Heat

A metal measuring tape expands when the temperature goes above 50°F. For every degree Fahrenheit above 50, its length increases by 0.00064%.

• The temperature is 100 degrees Fahrenheit. How much longer is a 30-foot measuring tape than its correct length?
• What is the percent error?

Lesson 14 Practice Problems

• A student estimated that it would take 3 hours to write a book report, but it actually took her 5 hours. What is the percent error for her estimate?
• A radar gun measured the speed of a baseball at 103 miles per hour. If the baseball was actually going 102.8 miles per hour, what was the percent error in this measurement?
• It took 48 minutes to drive downtown. An app estimated it would be less than that. If the error was 20%, what was the app’s estimate?
• A farmer estimated that there were 25 gallons of water left in a tank. If this is an underestimate by 16%, how much water was actually in the tank?
• For each story, write an equation that describes the relationship between the two quantities. a. Diego collected x kg of recycling. Lin collected 2/3 more than that. b. Lin biked x km. Diego biked 3/10 less than that. c. Diego read for x minutes. Lin read 4/7 of that.
• For each diagram, decide if y is an increase or a decrease of x. Then determine the percentage.
• Lin is making a window covering for a window that has the shape of a half circle on top of a square of side length 3 feet. How much fabric does she need?

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics .

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

How to Calculate Percent Error

Sample Percent Error Calculation

ThoughtCo / Nusha Ashjaee

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Percent error or percentage error expresses as a percentage the difference between an approximate or measured value and an exact or known value. It is used in science to report the difference between a measured or experimental value and a true or exact value. Here is how to calculate percent error, with an example calculation.

Key Points: Percent Error

• The purpose of a percent error calculation is to gauge how close a measured value is to a true value.
• Percent error (percentage error) is the difference between an experimental and theoretical value, divided by the theoretical value, multiplied by 100 to give a percent.
• In some fields, percent error is always expressed as a positive number. In others, it is correct to have either a positive or negative value. The sign may be kept to determine whether recorded values consistently fall above or below expected values.
• Percent error is one type of error calculation. Absolute and relative error are two other common calculations. Percent error is part of a comprehensive error analysis.
• The keys to reporting percent error correctly are to know whether or not to drop the sign (positive or negative) on the calculation and to report the value using the correct number of significant figures.

Percent Error Formula

Percent error is the difference between a measured or experiment value and an accepted or known value, divided by the known value, multiplied by 100%.

For many applications, percent error is always expressed as a positive value. The absolute value of the error is divided by an accepted value and given as a percent.

|accepted value - experimental value| \ accepted value x 100%

For chemistry and other sciences, it is customary to keep a negative value, should one occur. Whether error is positive or negative is important. For example, you would not expect to have positive percent error comparing actual to theoretical yield in a chemical reaction . If a positive value was calculated, this would give clues as to potential problems with the procedure or unaccounted reactions.

When keeping the sign for error, the calculation is the experimental or measured value minus the known or theoretical value, divided by the theoretical value and multiplied by 100%.

percent error = [experimental value - theoretical value] / theoretical value x 100%

Percent Error Calculation Steps

• Subtract one value from another. The order does not matter if you are dropping the sign (taking the absolute value. Subtract the theoretical value from the experimental value if you are keeping negative signs. This value is your "error."
• Divide the error by the exact or ideal value (not your experimental or measured value). This will yield a decimal number.
• Convert the decimal number into a percentage by multiplying it by 100.
• Add a percent or % symbol to report your percent error value.

Percent Error Example Calculation

In a lab, you are given a block of aluminum . You measure the dimensions of the block and its displacement in a container of a known volume of water. You calculate the density of the block of aluminum to be 2.68 g/cm 3 . You look up the density of a block of aluminum at room temperature and find it to be 2.70 g/cm 3 . Calculate the percent error of your measurement.

• Subtract one value from the other: 2.68 - 2.70 = -0.02
• Depending on what you need, you may discard any negative sign (take the absolute value): 0.02 This is the error.
• Divide the error by the true value:0.02/2.70 = 0.0074074
• Multiply this value by 100% to obtain the percent error: 0.0074074 x 100% = 0.74% (expressed using 2 significant figures ). Significant figures are important in science. If you report an answer using too many or too few, it may be considered incorrect, even if you set up the problem properly.

Percent Error Versus Absolute and Relative Error

Percent error is related to absolute error and relative error . The difference between an experimental and known value is the absolute error. When you divide that number by the known value you get relative error . Percent error is relative error multiplied by 100%. In all cases, report values using the appropriate number of significant digits.

• Bennett, Jeffrey; Briggs, William (2005),  Using and Understanding Mathematics: A Quantitative Reasoning Approach  (3rd ed.), Boston: Pearson.
• Törnqvist, Leo; Vartia, Pentti; Vartia, Yrjö (1985), "How Should Relative Changes Be Measured?",  The American Statistician ,  39  (1): 43–46.
• How to Calculate Experimental Error in Chemistry
• Absolute and Relative Error Calculation
• How to Calculate Percent
• The Relative Uncertainty Formula and How to Calculate It
• Percent Yield Definition and Formula
• Learn to Calculate Percent Change
• Relative Error Definition (Science)
• Absolute Error or Absolute Uncertainty Definition
• How to Calculate Mass Percent Composition
• How to Calculate Mass Percent
• Calculating the Concentration of a Chemical Solution
• Mass Percent Composition Problem
• Percent Composition by Mass Example
• How to Calculate Atomic Mass
• The GDP Deflator
• Tips and Rules for Determining Significant Figures

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Percent Error and Percent Increase Worksheets

What Is Percentage Error and Percentage Increase? - Whether it's profit on a sale item, error in a critical lab reading, or changes in the trends of a business' revenue, people need tools that can help them determine the changes and identify the patterns in the trend. There is one way you can calculate it and that is through percentages. Percentages are very helpful and the two methods that can be used to describe these changes are percentage errors and percentage change (increase or decrease). Percentage Error - Percentage error is the quantity which helps in determining the difference between the experimental and theoretical value. Step 1: Calculate the difference between the theoretical and experimental value Error = Theoretical value-Experimental Value. Step 2: Calculate the fractional change in the values. Fractional Change=(Theoretical Value-Experimental Value)/(Theoretical Value) Step 3: Multiply the fractional change by 100 to find the percentage error. Percentage Error=(theoretical Value-Experimental Value)/(Theoretical Value) × 100. Percentage Increase - The percentage increase is the value that compares the new increased value with the previous value. It can be calculated just like the percentage error. Step 1: Calculate the difference between the new and old value. Difference = New Value - Old Value. Step 2: Calculate the Fractional increase in the old value. Fractional Change = (New Value-Old Value)/(Old Value). Step 3: Multiply fractional change by 100. Fractional Change=(New Value-Old Value)/(Old Value)×100

Aligned Standard: Grade 7 Proportional Relationships - 7.RP.A.3

• Bed Sheets Error Step-by-step Lesson - Alan messed up his measurement of his bed sheets. How far was he off?
• Guided Lesson - Buying jelly cakes, yoga class, and table fan word problems.
• Guided Lesson Explanation - We work through the use of the percentage error calculation.
• Practice Worksheet - Can't anybody get something right? Calculate the level of the last ten errors I could dream up.
• Percent Word Problems Five Worksheet Pack - These word problems really range in length. Some are a paragraph, others are less than sentence.
• Matching Worksheet - Units and dollar signs are left off again.
• Answer Keys - These are for all the unlocked materials above.

Homework Sheets

See if you can try to help students focus in on the relationship between both of these skills.

• Homework 1 - John needs to purchase a blanket for his bedroom. John measured the blanket as 6 ft. The actual measurement was 5.5 ft. What is John’s percent error?
• Homework 2 - Liza was asked by the farmer to count all the cows. He counted a total of 120 cows. Liza did make a mistake in counting the cows and recorded the number as 160. What is Liza percent error?
• Homework 3 - Emma sold a hat for $20. Emma increases the price by 25%. What is the price of the hat now?

Practice Worksheets

Why are stores always increasing prices lately? Time to look at the math behind that.

• Practice 1 - Eva buys a guitar for $325. The store increases its purchase price by 20%? What is the new price of the guitar?
• Practice 2 - Soul wants to buy a ring for his wife. Soul calculates the amount of ring as $85.8. The actual price of ring is $80. What is Soul’s percent error?
• Practice 3 - Alisa calculates the cost of color box as $40. The actual price was $48. What is her percent error?

Math Skill Quizzes

I also throw in percentages of total in here to act as a ladder skill.

• Quiz 1 - Calculate 3% of 52.4 meters?
• Quiz 2 - A serving of chocolates cookies contains 1600 calories. One hundred thirty-five calories comes from fat. What percent of the total calories come from fat?
• Quiz 3 - Helen buys a shirt for $110. The store increases their purchase price by 25%? What is the new price?

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• Percent Error Worksheets

October 31, 2022

3 minutes read

When analyzing data, there is typically some error between the measured number and the actual one. The difference between an observed and an acceptable value is expressed as a percentage error. This topic may be complex for your kids; therefore, the percent of error worksheet with answers is a straightforward way of learning the concept.

Understanding the Concept of Percent Error

Percent Of Error Worksheet With Answers

Percent Error Practice Problems Worksheet Answers

Percentage Error Worksheet

Percent Error Worksheet PDF

Percent Error Worksheet 7Th Grade Answer Key

Percent Of Error Worksheet

Many factors, including human fallibility and the inherent uncertainties of estimating and measurement, might contribute to the erroneous result. These mistakes may be unnoticeable, hence the need to calculate percentage error.

Measurement mistakes occur due to inherent flaws in the measuring device and the human’s inherent limitations. There are varying degrees of inaccuracy, and occasionally, we have to judge if the mistake in our measurement is large enough to render the dimensions meaningless. Generally, a decreased margin of error suggests that we are getting closer to the correct number.

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Absolute error, or the difference between the observed and the actual value, is necessary for calculating percentage error. Divide the absolute error by the real value to get the relative error. To get the percentage error, multiply the relative value by 100.

Free Percent Error Practice Problems Worksheet Answers

The Brighterly percent error worksheet answer key is an excellent resource to help kids master the concept of percent error. These worksheets are designed by top professionals with knowledge of the idea and how to help kids learn.

Percent Error Worksheets PDF

Percent Error Worksheet

Percent Error Worksheet Answer Key

Percentage Error Worksheet Answer Key

Percent Error Worksheet PDF Answers

Using the percentage error worksheet answer key will help your kids master the concept of percentage error and is a way crosscheck the correctness of their answers. And your kids need to master the idea since this knowledge will be valuable throughout their school life and everyday life.

The printable percent error worksheet PDF answers will help students learn independently and repeatedly, thus leading to mastery.

More Percents Worksheets

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As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.

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Percentages Worksheets

Welcome to the percentages math worksheet page where we are 100% committed to providing excellent math worksheets. This page includes Percentages worksheets including calculating percentages of a number, percentage rates, and original amounts and percentage increase and decrease worksheets.

As you probably know, percentages are a special kind of decimal. Most calculations involving percentages involve using the percentage in its decimal form. This is achieved by dividing the percentage amount by 100. There are many worksheets on percentages below. In the first few sections, there are worksheets involving the three main types of percentage problems: calculating the percentage value of a number, calculating the percentage rate of one number compared to another number, and calculating the original amount given the percentage value and the percentage rate.

Most Popular Percentages Worksheets this Week

Percentage Calculations

Calculating the percentage value of a number involves a little bit of multiplication. One should be familiar with decimal multiplication and decimal place value before working with percentage values. The percentage value needs to be converted to a decimal by dividing by 100. 18%, for example is 18 ÷ 100 = 0.18. When a question asks for a percentage value of a number, it is asking you to multiply the two numbers together.

Example question: What is 18% of 2800? Answer: Convert 18% to a decimal and multiply by 2800. 2800 × 0.18 = 504. 504 is 18% of 2800.

• Calculating the Percentage Value (Whole Number Results) Calculating the Percentage Value (Whole Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Number Results) (Select percents) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Decimal Number Results) Calculating the Percentage Value (Decimal Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Number Results) (Select percents) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Whole Dollar Results) Calculating the Percentage Value (Whole Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Dollar Results) (Select percents) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Decimal Dollar Results) Calculating the Percentage Value (Decimal Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Dollar Results) (Select percents) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 25%)

Calculating what percentage one number is of another number is the second common type of percentage calculation. In this case, division is required followed by converting the decimal to a percentage. If the first number is 100% of the value, the second number will also be 100% if the two numbers are equal; however, this isn't usually the case. If the second number is less than the first number, the second number is less than 100%. If the second number is greater than the first number, the second number is greater than 100%. A simple example is: What percentage of 10 is 6? Because 6 is less than 10, it must also be less than 100% of 10. To calculate, divide 6 by 10 to get 0.6; then convert 0.6 to a percentage by multiplying by 100. 0.6 × 100 = 60%. Therefore, 6 is 60% of 10.

Example question: What percentage of 3700 is 2479? First, recognize that 2479 is less than 3700, so the percentage value must also be less than 100%. Divide 2479 by 3700 and multiply by 100. 2479 ÷ 3700 × 100 = 67%.

• Calculating the Percentage a Whole Number is of Another Whole Number Calculating the Percentage a Whole Number is of Another Whole Number (Percents from 1% to 99%) Calculating the Percentage a Whole Number is of Another Whole Number (Select percents) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 25%)
• Calculating the Percentage a Decimal Number is of a Whole Number Calculating the Percentage a Decimal Number is of a Whole Number (Percents from 1% to 99%) Calculating the Percentage a Decimal Number is of a Whole Number (Select percents) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 25%)
• Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Select percents) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 25%)
• Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Select percents) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 25%)

The third type of percentage calculation involves calculating the original amount from the percentage value and the percentage. The process involved here is the reverse of calculating the percentage value of a number. To get 10% of 100, for example, multiply 100 × 0.10 = 10. To reverse this process, divide 10 by 0.10 to get 100. 10 ÷ 0.10 = 100.

Example question: 4066 is 95% of what original amount? To calculate 4066 in the first place, a number was multiplied by 0.95 to get 4066. To reverse this process, divide to get the original number. In this case, 4066 ÷ 0.95 = 4280.

• Calculating the Original Amount from a Whole Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Whole Numbers ) Calculating the Original Amount (Select percents) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Whole Numbers )
• Calculating the Original Amount from a Decimal Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Decimals ) Calculating the Original Amount (Select percents) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Decimals )
• Calculating the Original Amount from a Whole Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
• Calculating the Original Amount from a Decimal Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )
• Mixed Percentage Calculations with Whole Number Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Whole Numbers )
• Mixed Percentage Calculations with Decimal Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Decimals ) Mixed Percentage Calculations (Select percents) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Decimals )
• Mixed Percentage Calculations with Whole Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
• Mixed Percentage Calculations with Decimal Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )

Percentage Increase/Decrease Worksheets

The worksheets in this section have students determine by what percentage something increases or decreases. Each question includes an original amount and a new amount. Students determine the change from the original to the new amount using a formula: ((new - original)/original) × 100 or another method. It should be straight-forward to determine if there is an increase or a decrease. In the case of a decrease, the percentage change (using the formula) will be negative.

• Percentage Increase/Decrease With Whole Number Percentage Values Percentage Increase/Decrease Whole Numbers with 1% Intervals Percentage Increase/Decrease Whole Numbers with 5% Intervals Percentage Increase/Decrease Whole Numbers with 25% Intervals
• Percentage Increase/Decrease With Decimal Number Percentage Values Percentage Increase/Decrease Decimals with 1% Intervals Percentage Increase/Decrease Decimals with 5% Intervals Percentage Increase/Decrease Decimals with 25% Intervals
• Percentage Increase/Decrease With Whole Dollar Percentage Values Percentage Increase/Decrease Whole Dollar Amounts with 1% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 5% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 25% Intervals
• Percentage Increase/Decrease With Decimal Dollar Percentage Values Percentage Increase/Decrease Decimal Dollar Amounts with 1% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 5% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 25% Intervals

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Explore the data: The full Suffolk/Globe poll results

S uffolk University and the Boston Globe partnered to poll 500 Massachusetts residents from April 16 to 20. The margin of error was plus or minus 4.4 percentage points.

Explore the data here.