Worked examples
The question
Question: what is the percent error, if the estimate is 50 and the actual value is 40?
estimate 50, actual 40
Percent error says how far off a guess is, as a percent of the real value.
error = how far off
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.
= error = 50 − 40 = 10
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.
= 1040
erroractual
Careful!
We divide by the actual value, 40.
Not by the guess.
The real value is what we compare with.
Careful: not 1050 = 20% ✗
3 Write it as a percent
10 and 40 can both be divided by 10.
That keeps the numbers small: 1/4.
= 14
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.
= 1 × 254 × 25 = 25100
25 out of 100 is 25%.
= 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.
25% of 40 = 0.25 × 40 = 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.
▶ Watch it solved
The question
Question: what is the percent error, if the estimate is 23 and the actual value is 30?
estimate 23, actual 30
Percent error says how far off a guess is, as a percent of the real value.
error = how far off
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.
= error = 30 − 23 = 7
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.
= 730
erroractual
Careful!
We divide by the actual value, 30.
Not by the guess.
The real value is what we compare with.
Careful: not 723 = 30.4% ✗
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%.
= 7 × 10030%
700 divided by 30 is about 23.3.
700 ÷ 30 = 23.3…
To the nearest tenth of a percent, it is 23.3%.
= ≈ 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.
23.3% of 30 = 0.233 × 30 = 6.99
6.99 is very close to 7: we rounded.
So the answer is right!
6.99 ≈ 7
Let's look back.
First: find the error.
Then: compare with the actual.
Then: write it as a percent.
Last: check.
▶ Watch it solved
The question
Question: what is the percent error, if Maya guessed 30 jelly beans and there were really 25?
Maya: 30 actual: 25
Percent error says how far off a guess is, as a percent of the real value.
error = how far off
1 Find the error
First: how far off is it?
The bigger one minus the smaller one.
30 minus 25 is 5.
The error is never negative: it is a distance.
= error = 30 − 25 = 5
2 Compare with the actual
Now we compare the error with the real value.
The error, 5, goes on top.
The actual value, 25, goes at the bottom.
= 525
erroractual
Careful!
We divide by the actual value, 25.
Not by the guess.
The real value is what we compare with.
Careful: not 530 = 16.7% ✗
3 Write it as a percent
5 and 25 can both be divided by 5.
That keeps the numbers small: 1/5.
= 15
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.
= 1 × 205 × 20 = 20100
20 out of 100 is 20%.
= 20%
So the percent error is 20%.
The guess 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 25 is 5.
20% of 25 = 0.2 × 25 = 5
That is the error, 5.
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.
▶ Watch it solved
