How To Calculate Percent Error?

Have you ever played the gumball machine game at a school or a carnival? It is the game where you must make your best-estimated guesses at how many gumballs you think there are. The individual who guesses closest to the actual number of gumballs wins the prize.

Again, think about it. One day James measured his height and found 6 feet. However, after careful observation, he later found his true height to be 5.7 feet. So, how to find the error James made in measuring his height or how to guess the actual number of gumballs in the machine? This calculation is what percent error is all about.

In science and mathematics-related matters, the concept of percent error is often used wherein the variance between the experimental value and the exact value needs to be determined. Eminent practitioners in these fields, as well as other professionals who conduct experiments or surveys, may develop a hypothesis on its basis to see how far off their idea could be from the actual result of the investigation.

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If you are one of those million students striving to accurately calculate percentage error, then reading this post will surely put you miles ahead. Here we will walk you through the definition of percent error and steps to calculate the percent error remarkably like never before!

Let’s get started!

Percent Error: A Quick Overview

According to the best minds of math assignment help services, percent error, or percentage error, is an expression of the difference between a measured value and the known or accepted value. It is also generally used in science to report the difference between experimental and expected values.

All in all, one gets to track down the difference between the true response and the speculated reply, partition it by the true response, and express it as a percentage. Percent errors also indicate how huge our errors are at the point when we measure something.

For instance, a 3% error indicates that we got extremely near the acknowledged value, while 80% indicates that we were far from the actual value.

Formula To Calculate Percent Error

The formula for finding ‘percentage error’ or ‘percent error’ is=

 

|Approximate Value − Exact Value|	× 100%
|Exact Value|

Here, the | symbol implies absolute value, so negative becomes positive

Crucial Steps To Calculate Percent Error

• Write Down The Formula For Percentage Error

As we said before, the formula for calculating percentage error is incredibly simple.

|Approximate Value − Exact Value|	× 100%
|Exact Value|

You will need to use this as a reference to plug in the two values you need to know. The approximate value is the estimated value, and the exact value is the real value. For example,  if you guess there will be 8 oranges in the bag, but there are 10, 8 is the approximate value, and 10 is the exact value.

• Subtract The Exact Values From The Approximate One

In the above-mentioned example of oranges, you will require subtracting 10 (the exact value) from 8 (estimated value). In this case, the result is 8-10= -2.

The difference denotes the magnitude of difference in approximate and estimated values. This begins to explain how far off the results were from what they were expected to be.

• Find The Absolute Value of The Top Result

Since the formula for calculating percent error uses the absolute value of the difference, you can discard the negative sign. In this example, -1 will become just 1.

In the above-mentioned example of oranges, 9-10= -1. The absolute value of -1, presented as |-1| is 1. If your results are positive, leave the number as it is.

• Use Absolute Value To Divide The Result

Make sure to divide the top number by the absolute value of your exact variable, either with a calculator or manually. In this example of orange, the exact value is already positive, so you simply need to divide 1 by 10.

1/ |10|= 1/10

In certain cases, the exact value can be a negative number. If this happens to be the case, you should ignore the negative.

• Convert The Fraction Into Decimal Form

It is easiest to have a decimal number to convert the fraction into a percentage. Like 1/10= 0.1. If you cannot use a calculator,  use long division to convert the fraction to the decimal.

• Multiply The Result Times 100

Now, just multiply the result- 0.1 by 100. This will enable you to convert the answer into percentage form. Simply add the percentage symbol to the answer, and you will be done.

Like, 0.1 *100= 10. Add the percent sign to get 10% as your percent error.

• Check Your Work To Ensure The Answer Is Correct

Often, swapping signs (positive/negative) and dividing can result in minor errors in your calculations. It is always wise to check if your answer makes sense.

In the aforementioned example, we aim to ensure our estimation of 9 oranges is off by 10% of the actual value of the oranges. 10%  (10%= 0.1) of 10 oranges is 1(0.1 *10=1)

Thus, 9 +1= 10 oranges. This confirms our guess of 9 was truly off by just 1 orange or 10% of the actual value of 10 oranges.

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Example Questions

1. Anne's English class had 34 children yesterday. She made an error in estimating the class total and recorded it as 28 children. What is her percent error?

Solution=

The actual number of students= 34

Estimated number of students = 28

Absolute error= 34-28= 6

Percent error= 6/28= 0.21 =21%

Thus, the percent error made by Anna is 21%

2. A boy measured the area of the rectangle plot to be 500 cm². However, the actual area of the plot was recorded as 495 cm². Evaluate the percent error of his measurement.

Solution:

Measured area value= 500 cm²

Actual area value =495 cm²

Steps of Calculation-

Subtract one value from another, 500-495= 5. Here the difference is 5, which is the error.

Now divide the error by actual value= 5/495= 0.101010

Multiply this value by 100

0.101010*100= 1.010

Hence, 1.01% is the percent error.

3. Mary believed 90 people would attend the concert, but 100 attended. What would be Mary's percent error?

Solution:

The actual number of people who attended the concert= 100

The number of people Mary believed will attend= 90

Error= Expected number of people attended- Actual number of people

100=90= 10

Applying the formula,

Percent Error= (Error / (Actual Measurement) *100

= (10/90) *100= 0.235*100= 23.5

Percent error= 23.5%

While solving problems on percent error can give countless students a hard time, this blog could be the answer to it all. Save this post. Take the help of this guide to form an in-depth understanding and sail through your percent error problems like a champion!

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