A rectangle is 9 m by 3 m, both to the nearest m. Find the upper…

Step by step, with the reason for every step · Bounds in calculations · Foundations

Step by step

The question

Question: A rectangle is 9 m by 3 m, both to the nearest m.

Find the upper bound of its perimeter.

1 Bounds of each number

The length is 9 m, to the nearest m.

Half a step is 0.5.

So it is from 8.5 up to 9.5.

8.5 ≤ length < 9.5

9 ± 0.5

The width is 3 m, to the nearest m.

Half a step is 0.5.

So it is from 2.5 up to 3.5.

2.5 ≤ width < 3.5

3 ± 0.5

2 Choose the bounds

To make the perimeter as big as it can be, both numbers must be as big as they can be.

So we use 9.5 and 3.5.

upper bound = 2 × (9.5 + 3.5)

biggest: biggest + biggest

Careful!

We do not change the answer by half a step.

We work it out again with the biggest numbers.

Careful: not 24 + 0.5 ✗

3 Work it out

That is 26 m.

upper bound = 26 m

9.5 plus 3.5 is 13.

Two times that is 26.

9.5 + 3.5 = 13

2 × 13 = 26

So the upper bound of the perimeter is 26 m.

4 Check

Let's check.

With the rounded numbers we get 24.

with the rounded numbers: 2 × (9 + 3) = 24

The upper bound, 26, is more than that, as it should be.

So the answer is right!

26 is more than 24

Let's look back.

First: bounds of each number.

Then: choose the bounds.

Then: work it out.

Last: check.

Answer

2 × 13 = 26

Your turn

Try this one yourself, then check:

Show the answer

upper bound = 38 m

More from Bounds in calculations

The whole lesson: Bounds in calculations →