Step by step
The question
Question: what is the percent error, if the measurement is 9.5 cm and the actual value is 10 cm?
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.
10 minus 9.5 is 0.5.
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, 0.5, 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.
Decimals are hard to work with.
So we multiply the top and the bottom by 10.
Times 10/10 is times 1: the size stays.
3 Write it as a percent
Percent means out of 100.
The bottom is 100 already.
So it is 5%.
So the percent error is 5%.
The measurement was 5% too low.
4 Check
Let's check: 5% of the actual value should give the error.
5% is 0.05.
0.05 times 10 is 0.5.
That is the error, 0.5.
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.