A height is 14 m to the nearest m Step by Step

Step by step

The question

Question: the height is 14 m, to the nearest m.

Find the upper and lower bounds.

Height: 14 m, to the nearest m

The real height was rounded.

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

1 Find the step

It was rounded to the nearest m.

So the step is 1 m.

step = 1 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 14.

Half of 1 is 0.5.

half a step = 1 ÷ 2 = 0.5 m

3 Find the bounds

The lower bound is 14 minus 0.5: 13.5.

lower bound = 14 − 0.5 = 13.5 m

Careful!

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

13 would round to 13, not to 14.

Careful: not 13 to 15 ✗

The upper bound is 14 plus 0.5: 14.5.

upper bound = 14 + 0.5 = 14.5 m

4 Show it on a number line

So 13.5 ≤ height < 14.5.

This is called the error interval.

13.5 ≤ height < 14.5

5 Check

Let's check.

13.5, rounded to the nearest m, is 14.

13.5 rounds to 14

And 14.49, just under the upper bound, also rounds to 14.

So the bounds are right!

14.49 rounds to 14

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