Estimate 90, actual 100, percent error Step by Step

Step by step

The question

Question: what is the percent error, if the estimate is 90 and the actual value is 100?

estimate 90, actual 100

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.

100 minus 90 is 10.

The error is never negative: it is a distance.

= error = 100 − 90 = 10

2 Compare with the actual

Now we compare the error with the real value.

The error, 10, goes on top.

The actual value, 100, goes at the bottom.

= 10100

erroractual

Careful!

We divide by the actual value, 100.

Not by the guess.

The real value is what we compare with.

Careful: not 1090 = 11.1% ✗

3 Write it as a percent

Percent means out of 100.

The bottom is 100 already.

So it is 10%.

= 10%

So the percent error is 10%.

The estimate was 10% too low.

4 Check

Let's check: 10% of the actual value should give the error.

10% is 0.1.

0.1 times 100 is 10.

10% of 100 = 0.1 × 100 = 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.

Answer