Step by step
The question
Question: x = 15.2 and y = 9.7, both to 1 decimal place.
Find the upper bound of x − y.
1 Bounds of each number
The number x is 15.2, to 1 decimal place.
Half a step is 0.05.
So it is from 15.15 up to 15.25.
15.15 ≤ x < 15.25
15.2 ± 0.05
The number y is 9.7, to 1 decimal place.
Half a step is 0.05.
So it is from 9.65 up to 9.75.
9.65 ≤ y < 9.75
9.7 ± 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.
So we use 15.25 and 9.65.
upper bound = 15.25 − 9.65
biggest: biggest − smallest
Careful!
Taking away a bigger number makes the answer smaller.
Careful: not 15.25 − 9.75 ✗
3 Work it out
That is 5.6.
upper bound = 5.6
So the upper bound of the answer is 5.6.
4 Check
Let's check.
With the rounded numbers we get 5.5.
with the rounded numbers: 15.2 − 9.7 = 5.5
The upper bound, 5.6, is more than that, as it should be.
So the answer is right!
5.6 is more than 5.5
Let's look back.
First: bounds of each number.
Then: choose the bounds.
Then: work it out.
Last: check.
Answer
upper bound = 5.6