A rectangle is 6 cm by 4 cm, both to the nearest cm. Find the lower… Step by Step

Step by step

The question

Question: A rectangle is 6 cm by 4 cm, both to the nearest cm.

Find the lower bound of its area.

1 Bounds of each number

The length is 6 cm, to the nearest cm.

Half a step is 0.5.

So it is from 5.5 up to 6.5.

5.5 ≤ length < 6.5

6 ± 0.5

The width is 4 cm, to the nearest cm.

Half a step is 0.5.

So it is from 3.5 up to 4.5.

3.5 ≤ width < 4.5

4 ± 0.5

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 5.5 and 3.5.

lower bound = 5.5 × 3.5

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 24 − 0.5 ✗

3 Work it out

That is 19.25 cm².

lower bound = 19.25 cm²

To multiply decimals: first 55 times 35, as whole numbers.

That is 1925.

Then count the decimal places: 2.

55 × 35 = 1925

2 decimal places: 19.25

So the lower bound of the area is 19.25 cm².

4 Check

Let's check.

With the rounded numbers we get 24.

with the rounded numbers: 6 × 4 = 24

The lower bound, 19.25, is less than that, as it should be.

So the answer is right!

19.25 is less than 24

Let's look back.

First: bounds of each number.

Then: choose the bounds.

Then: work it out.

Last: check.

Answer