x = 2.5 and y = 0.8, both to 1 decimal place. Find the upper bound… Step by Step

Step by step

The question

Question: x = 2.5 and y = 0.8, both to 1 decimal place.

Find the upper bound of x × y.

1 Bounds of each number

The number x is 2.5, to 1 decimal place.

Half a step is 0.05.

So it is from 2.45 up to 2.55.

2.45 ≤ x < 2.55

2.5 ± 0.05

The number y is 0.8, to 1 decimal place.

Half a step is 0.05.

So it is from 0.75 up to 0.85.

0.75 ≤ y < 0.85

0.8 ± 0.05

2 Choose the bounds

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

So we use 2.55 and 0.85.

upper bound = 2.55 × 0.85

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 2 + 0.05 ✗

3 Work it out

That is 2.1675.

upper bound = 2.1675

To multiply decimals: first 255 times 85, as whole numbers.

That is 21675.

Then count the decimal places: 4.

255 × 85 = 21675

4 decimal places: 2.1675

So the upper bound of the answer is 2.1675.

4 Check

Let's check.

With the rounded numbers we get 2.

with the rounded numbers: 2.5 × 0.8 = 2

The upper bound, 2.1675, is more than that, as it should be.

So the answer is right!

2.1675 is more than 2

Let's look back.

First: bounds of each number.

Then: choose the bounds.

Then: work it out.

Last: check.

Answer