Step by step
The question
Question: what is the percent error, if Ana guessed 210 marbles and there were really 175?
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.
210 minus 175 is 35.
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, 35, goes on top.
The actual value, 175, goes at the bottom.
Careful!
We divide by the actual value, 175.
Not by the guess.
The real value is what we compare with.
3 Write it as a percent
35 and 175 can both be divided by 35.
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 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 175 is 35.
That is the error, 35.
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.