Percent Error

Sometimes we make an estimate or a guess and then later find out that we were a little off. We can calculate just how much we were off using percent error.

Here is the formula we use for determining the percent error:

x 100

Example 1:

Hillary estimated that there were about 130 shoppers at her store today. However, there were actually 135. What is her percent error?

What do we know?

Estimate = 130

Actual = 135

Difference between actual and estimate = 135 - 130 = 5.

Now we are ready to determine the percent error.

Example 2:

Carlos guesses that he has been running for 38 minutes. He has actually only been running for 32 minutes. Determine his percent error.

What do we know?

Estimate = 38 minutes

Actual = 32 minutes

Difference: 38 - 32 = 6 minutes

(The difference should always be a positive amount.)

Example 3:

Sunil measured the piece of wood to be 14 cm long. It was actually 17 cm long. What is the percent error?

What do we know?

Estimate = 14 cm

Actual = 17 cm

Difference: 17 - 14 = 3 cm

Example 4:

Susan estimated that the coin would land on heads 400 times. It actually landed on heads 320 times. Determine the percent error.

What do we know?

Estimate = 400 times

Actual = 320 times

Difference = 400 - 320 = 80 times

So why is percent error important?

Mathematicians and scientists like to find out if the theoretical ideas are close to the actual results. They can use the percent error to help determine the relationship between what actually happened and what they expected to happen.