A rectangle is 4.2 m by 2.5 m, both to 1 decimal place. Find the… Step by Step

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The question

Question: A rectangle is 4.2 m by 2.5 m, both to 1 decimal place.

Find the upper bound of its area.

1 Bounds of each number

The length is 4.2 m, to 1 decimal place.

Half a step is 0.05.

So it is from 4.15 up to 4.25.

4.15 ≤ length < 4.25

4.2 ± 0.05

The width is 2.5 m, to 1 decimal place.

Half a step is 0.05.

So it is from 2.45 up to 2.55.

2.45 ≤ width < 2.55

2.5 ± 0.05

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 4.25 and 2.55.

upper bound = 4.25 × 2.55

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 10.5 + 0.05 ✗

3 Work it out

That is 10.8375 m².

upper bound = 10.8375 m²

To multiply decimals: first 425 times 255, as whole numbers.

That is 108375.

Then count the decimal places: 4.

425 × 255 = 108375

4 decimal places: 10.8375

So the upper bound of the area is 10.8375 m².

4 Check

Let's check.

With the rounded numbers we get 10.5.

with the rounded numbers: 4.2 × 2.5 = 10.5

The upper bound, 10.8375, is more than that, as it should be.

So the answer is right!

10.8375 is more than 10.5

Let's look back.

First: bounds of each number.

Then: choose the bounds.

Then: work it out.

Last: check.

Answer