A length is 12.08 m to 2 decimal places Step by Step

Step by step

The question

Question: the length is 12.08 m, to 2 decimal places.

Find the upper and lower bounds.

Length: 12.08 m, to 2 decimal places

The real length was rounded.

We want the smallest and the biggest it could have been.

1 Find the step

2 decimal places: we rounded to the nearest 0.01.

So the step is 0.01.

step = 0.01 m

upper bound = the biggest it could be

lower bound = the smallest it could be

2 Half a step

Anything less than half a step away rounds to 12.08.

Half of 0.01 is 0.005.

half a step = 0.01 ÷ 2 = 0.005 m

3 Find the bounds

The lower bound is 12.08 minus 0.005: 12.075.

lower bound = 12.08 − 0.005 = 12.075 m

Careful!

We go only half a step down and half a step up.

12.07 would round to 12.07, not to 12.08.

Careful: not 12.07 to 12.09 ✗

The upper bound is 12.08 plus 0.005: 12.085.

upper bound = 12.08 + 0.005 = 12.085 m

4 Show it on a number line

So 12.075 ≤ length < 12.085.

This is called the error interval.

12.075 ≤ length < 12.085

5 Check

Let's check.

12.075, rounded to 2 decimal places, is 12.08.

12.075 rounds to 12.08

And 12.084, just under the upper bound, also rounds to 12.08.

So the bounds are right!

12.084 rounds to 12.08

Let's look back.

First: find the step.

Then: half a step.

Then: find the bounds.

Then: show it on a number line.

Last: check.

Answer