Step by step
The question
Question: what is the percent error, if the estimate is 23 and the actual value is 30?
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.
30 minus 23 is 7.
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, 7, goes on top.
The actual value, 30, goes at the bottom.
Careful!
We divide by the actual value, 30.
Not by the guess.
The real value is what we compare with.
3 Write it as a percent
Percent means out of 100.
30 does not go into 100.
100% is all of it: 1 whole.
Times 1 does not change the size.
So we multiply by 100%.
700 divided by 30 is about 23.3.
To the nearest tenth of a percent, it is 23.3%.
So the percent error is about 23.3%.
The estimate was 23.3% too low.
4 Check
Let's check: 23.3% of the actual value should give the error.
23.3% is 0.233.
0.233 times 30 is 6.99.
6.99 is very close to 7: we rounded.
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.