A rectangle is 3.6 cm by 1.4 cm, both to 1 decimal place. Find the… Step by Step

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The question

Question: A rectangle is 3.6 cm by 1.4 cm, both to 1 decimal place.

Find the lower bound of its area.

1 Bounds of each number

The length is 3.6 cm, to 1 decimal place.

Half a step is 0.05.

So it is from 3.55 up to 3.65.

3.55 ≤ length < 3.65

3.6 ± 0.05

The width is 1.4 cm, to 1 decimal place.

Half a step is 0.05.

So it is from 1.35 up to 1.45.

1.35 ≤ width < 1.45

1.4 ± 0.05

2 Choose the bounds

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

So we use 3.55 and 1.35.

lower bound = 3.55 × 1.35

smallest: smallest × smallest

Careful!

We do not change the answer by half a step.

We work it out again with the smallest numbers.

Careful: not 5.04 − 0.05 ✗

3 Work it out

That is 4.7925 cm².

lower bound = 4.7925 cm²

To multiply decimals: first 355 times 135, as whole numbers.

That is 47925.

Then count the decimal places: 4.

355 × 135 = 47925

4 decimal places: 4.7925

So the lower bound of the area is 4.7925 cm².

4 Check

Let's check.

With the rounded numbers we get 5.04.

with the rounded numbers: 3.6 × 1.4 = 5.04

The lower bound, 4.7925, is less than that, as it should be.

So the answer is right!

4.7925 is less than 5.04

Let's look back.

First: bounds of each number.

Then: choose the bounds.

Then: work it out.

Last: check.

Answer