x = 7.2 and y = 3.5, both correct to 1 decimal place. Find the upper… Step by Step

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The question

Question: x = 7.2 and y = 3.5, both to 1 decimal place.

Find the upper bound of x − y.

1 Bounds of each number

The number x is 7.2, to 1 decimal place.

Half a step is 0.05.

So it is from 7.15 up to 7.25.

7.15 ≤ x < 7.25

That is 7.2, plus or minus 0.05.

7.2 ± 0.05

The number y is 3.5, to 1 decimal place.

Half a step is 0.05.

So it is from 3.45 up to 3.55.

3.45 ≤ y < 3.55

That is 3.5, plus or minus 0.05.

3.5 ± 0.05

2 Choose the bounds

Taking away a smaller number leaves more.

So the biggest answer is the biggest x minus the smallest y.

biggest: biggest − smallest

So we use 7.25 and 3.45.

upper bound = 7.25 − 3.45

Careful!

Taking away a bigger number makes the answer smaller.

Careful: not 7.25 − 3.55 ✗

3 Work it out

7.25 minus 3.45 is 3.8.

7.25 − 3.45 = 3.8

So it is 3.8.

upper bound = 3.8

So the upper bound of the answer is 3.8.

4 Check

Let's check.

With the rounded numbers we get 3.7.

with the rounded numbers: 7.2 − 3.5 = 3.7

The upper bound, 3.8, is more than that, as it should be.

So the answer is right!

3.8 is more than 3.7

Let's look back.

First: bounds of each number.

Then: choose the bounds.

Then: work it out.

Last: check.

Answer