Estimate 140, actual 200, percent error Step by Step

Step by step

The question

Question: what is the percent error, if the estimate is 140 and the actual value is 200?

estimate 140, actual 200

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.

200 minus 140 is 60.

The error is never negative: it is a distance.

= error = 200 − 140 = 60

2 Compare with the actual

Now we compare the error with the real value.

The error, 60, goes on top.

The actual value, 200, goes at the bottom.

= 60200

erroractual

Careful!

We divide by the actual value, 200.

Not by the guess.

The real value is what we compare with.

Careful: not 60140 = 42.9% ✗

3 Write it as a percent

60 and 200 can both be divided by 20.

That keeps the numbers small: 3/10.

= 310

Percent means out of 100.

10 times 10 is 100.

So we multiply the top and the bottom by 10.

3 times 10 is 30.

= 3 × 1010 × 10 = 30100

30 out of 100 is 30%.

= 30%

So the percent error is 30%.

The estimate was 30% too low.

4 Check

Let's check: 30% of the actual value should give the error.

30% is 0.3.

0.3 times 200 is 60.

30% of 200 = 0.3 × 200 = 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