A rectangle is 20 cm by 15 cm, both to the nearest 5 cm. Find the… Step by Step

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The question

Question: A rectangle is 20 cm by 15 cm, both to the nearest 5 cm.

Find the upper bound of its area.

1 Bounds of each number

The length is 20 cm, to the nearest 5 cm.

Half a step is 2.5.

So it is from 17.5 up to 22.5.

17.5 ≤ length < 22.5

20 ± 2.5

The width is 15 cm, to the nearest 5 cm.

Half a step is 2.5.

So it is from 12.5 up to 17.5.

12.5 ≤ width < 17.5

15 ± 2.5

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 22.5 and 17.5.

upper bound = 22.5 × 17.5

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 300 + 2.5 ✗

3 Work it out

That is 393.75 cm².

upper bound = 393.75 cm²

To multiply decimals: first 225 times 175, as whole numbers.

That is 39375.

Then count the decimal places: 2.

225 × 175 = 39375

2 decimal places: 393.75

So the upper bound of the area is 393.75 cm².

4 Check

Let's check.

With the rounded numbers we get 300.

with the rounded numbers: 20 × 15 = 300

The upper bound, 393.75, is more than that, as it should be.

So the answer is right!

393.75 is more than 300

Let's look back.

First: bounds of each number.

Then: choose the bounds.

Then: work it out.

Last: check.

Answer