Estimate 300, actual 240, percent error Step by Step

Step by step

The question

Question: what is the percent error, if the estimate is 300 and the actual value is 240?

estimate 300, actual 240

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.

300 minus 240 is 60.

The error is never negative: it is a distance.

= error = 300 − 240 = 60

2 Compare with the actual

Now we compare the error with the real value.

The error, 60, goes on top.

The actual value, 240, goes at the bottom.

= 60240

erroractual

Careful!

We divide by the actual value, 240.

Not by the guess.

The real value is what we compare with.

Careful: not 60300 = 20% ✗

3 Write it as a percent

60 and 240 can both be divided by 60.

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 240 is 60.

25% of 240 = 0.25 × 240 = 60

That is the error, 60.

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