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Algebra for Kids2 chapters | 6 lessons

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Lesson Transcript

In this lesson, we'll define what percentage error is, why it is useful, and how to calculate it. We'll also look at some examples of when you could use percentage error.

Look closely at the image of the gumball machine and make your best estimated guess at how many gumballs you think there are.

Have you ever played this game at school or at a carnival? The person who guesses closest to the actual number of gumballs wins a prize. We're going to explore how to calculate the winner by learning about percentage error.

**Percentage error** is the difference between the estimated number and the actual number when compared to the actual number expressed in percent format. The formula looks like this:

In other words, you take the difference between the real answer and the guessed answer, divide it by the real answer, and then turn it into a percent.

For example, let's say you guessed that there were 230 gumballs in the image, but there were actually 311 gumballs. The difference between your guess (230) and the actual number (311) in comparison to the actual number (311) expressed as a percent is the percentage error.

Did you notice the straight lines that were part of our formula? They indicate that you take the **absolute value** of that number, or the distance of a number from zero, without regard for negative signs. This simply means that if you get a negative number inside the absolute value signs, you treat it as if it were positive.

To calculate percentage error, you subtract the actual number from the estimated number to find the error. Then, you divide the error in absolute value by the actual number in absolute value. This gives you the error in a decimal format. From there, you can multiply by 100% to find the percentage error.

Let's plug the proposed example into the equation. You guessed that there were 230 gumballs, but there were actually 311 gumballs.

The first step is to subtract the actual number (311) from the estimated number (230), which gives us an error of the absolute value of -81. Next, we divide the absolute value of -81 by the absolute value of 311 and get 0.26. Since -81 is in absolute value, we treat it as just 81. Finally, we multiply 0.26 by 100% to get 26%. Your guess was off by 26%, the percentage error.

You are in charge of calculating the percentage error for each participant to see who wins the prize. The guesses are as follows:

- Mario: 376
- Erin: 217
- Tina: 299

Try to calculate the percentage error for each person on your own before looking at the solution.

After some calculations, you find that Mario's guess was 21% off from the actual number.

Erin's guess is next. Erin's guess was off by 30% and was the farthest away from the actual number.

And, finally, you calculate for Tina's guess, which, turns out, was only off by 4%, very close to the actual value. She is the winner!!

**Percentage error** is a way of calculating how far an estimated number was from the actual number in terms of a percentage. The formula for percentage error is:

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Additional Activities

Percentage error is a way to analyze how successful an experiment was. It is used in many physical sciences including chemistry and physics experiments. Let's work on some scenarios where we can practice using the percentage error equation.

1. A student is measuring the amount of water in a graduated cylinder and reports a value of 24 mL. The teacher reports the value as 24.2 mL. What is the student's percent error?

2. Another student was experimentally determining the boiling point of water. They reported it to be 99.5° C. The accepted value for the boiling point of water is 100° C. What is the percent error?

3. The percent error of a student's measurement of the density of aluminum is -4.2%. The accepted value of the density of aluminum is 2.7 g/cm3. What is the student's value for the density of aluminum?

The percentage error formula is % error = (|experimental - accepted|) / (accepted) x 100.

1. (|24 - 24.2|) / 24.2) x 100 = 0.83% error

2. (|99.5 - 100|) / 100 x 100 = 0.5% error

3. -0.042 = (x - 2.7) / 2.7

-0.1134 = x - 2.7

2.59 g/cm3 = x

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Algebra for Kids2 chapters | 6 lessons

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