Step by step
The question
Question: what is the percent error, if the estimate is 12 and the actual value is 10?
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.
12 minus 10 is 2.
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, 2, goes on top.
The actual value, 10, goes at the bottom.
Careful!
We divide by the actual value, 10.
Not by the guess.
The real value is what we compare with.
3 Write it as a percent
2 and 10 can both be divided by 2.
That keeps the numbers small: 1/5.
Percent means out of 100.
5 times 20 is 100.
So we multiply the top and the bottom by 20.
1 times 20 is 20.
20 out of 100 is 20%.
So the percent error is 20%.
The estimate was 20% too high.
4 Check
Let's check: 20% of the actual value should give the error.
20% is 0.2.
0.2 times 10 is 2.
That is the error, 2.
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.