Step by step
The question
Question: what is the percent error, if the estimate is 50 and the actual value is 40?
Percent error says how far off a guess is, as a percent of the real value.
1 Find the error
First: how far off is it?
The bigger one minus the smaller one.
50 minus 40 is 10.
The error is never negative: it is a distance.
2 Compare with the actual
Now we compare the error with the real value.
The error, 10, goes on top.
The actual value, 40, goes at the bottom.
Careful!
We divide by the actual value, 40.
Not by the guess.
The real value is what we compare with.
3 Write it as a percent
10 and 40 can both be divided by 10.
That keeps the numbers small: 1/4.
Percent means out of 100.
4 times 25 is 100.
So we multiply the top and the bottom by 25.
1 times 25 is 25.
25 out of 100 is 25%.
So the percent error is 25%.
The estimate was 25% too high.
4 Check
Let's check: 25% of the actual value should give the error.
25% is 0.25.
0.25 times 40 is 10.
That is the error, 10.
So the answer is right!
Let's look back.
First: find the error.
Then: compare with the actual.
Then: write it as a percent.
Last: check.