A rectangle is 8 cm by 5 cm, both to the nearest cm. Find the upper… Step by Step

Step by step

The question

Question: A rectangle is 8 cm by 5 cm, both to the nearest cm.

Find the upper bound of its area.

1 Bounds of each number

The length is 8 cm, to the nearest cm.

Half a step is 0.5.

So it is from 7.5 up to 8.5.

7.5 ≤ length < 8.5

8 ± 0.5

The width is 5 cm, to the nearest cm.

Half a step is 0.5.

So it is from 4.5 up to 5.5.

4.5 ≤ width < 5.5

5 ± 0.5

2 Choose the bounds

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

So we use 8.5 and 5.5.

upper bound = 8.5 × 5.5

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 40 + 0.5 ✗

3 Work it out

That is 46.75 cm².

upper bound = 46.75 cm²

To multiply decimals: first 85 times 55, as whole numbers.

That is 4675.

Then count the decimal places: 2.

85 × 55 = 4675

2 decimal places: 46.75

So the upper bound of the area is 46.75 cm².

4 Check

Let's check.

With the rounded numbers we get 40.

with the rounded numbers: 8 × 5 = 40

The upper bound, 46.75, is more than that, as it should be.

So the answer is right!

46.75 is more than 40

Let's look back.

First: bounds of each number.

Then: choose the bounds.

Then: work it out.

Last: check.

Answer