When calculating percent error, just take the ratio of the amount of error to the accepted value or true value, or real value.
Then, convert the ratio to a percent.
We can expresss the percent error with the following formula shown below:
The amount of error is a subtraction between the measured value and the accepted value
Keep in mind that when computing the amount of error, you are always looking for a positive value.
Therefore, always subtract the smaller value from the bigger. In other words, amount of error = bigger − smaller
Percent error word problem #1
A student made a mistake when measuring the volume of a big container. He found the volume to be 65 liters.
However, the real value for the volume is 50 liters. What is the percent error?
Percent error = (amount of error)/accepted value
amount of error = 65 - 50 = 15
The accepted value is obviously the real value for the volume, which 50
So, percent error = 15/50
Just convert 15/50 to a percent. We can do this multiplying both the numerator and the denominator by 2
We get (15 × 2)/(50 × 2) = 30/100 = 30%
Notice that in the problem above, if the true value was 65 and the measured value was 50, you will still do
65 − 50 to get the amount of error, so your answer is still positive as already stated
However, be careful! The accepted value is 65, so your percent error is 15/65 = 0.2307 = 0.2307/1 = (0.2307 × 100)/(1 × 100) = 23.07/100 = 23.07%
Percent error word problem #2
A man measured his height and found 6 feet. However, after he carefully measured his height a second time, he found his real height to be 5 feet.
What is the percent error the man made the first time he measured his height?
Percent error = (amount of error)/accepted value
amount of error = 6 - 5 = 1
The accepted value is the man's real height or the value he found after he carefully measured his height, or 5
So, percent error = 1/5
Just convert 1/5 to a percent. We can do this multiplying both the numerator and the denominator by 20
We get (1 × 20)/(5 × 20) = 20/100 = 20%
I hope what I explained above was enough to help you understand what to do when calculating percent error