Step by step
The question
Question: x = 9.4 and y = 3.2, both to 1 decimal place.
Find the upper bound of x − y.
1 Bounds of each number
The number x is 9.4, to 1 decimal place.
Half a step is 0.05.
So it is from 9.35 up to 9.45.
9.35 ≤ x < 9.45
9.4 ± 0.05
The number y is 3.2, to 1 decimal place.
Half a step is 0.05.
So it is from 3.15 up to 3.25.
3.15 ≤ y < 3.25
3.2 ± 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 9.45 and 3.15.
upper bound = 9.45 − 3.15
biggest: biggest − smallest
Careful!
Taking away a bigger number makes the answer smaller.
Careful: not 9.45 − 3.25 ✗
3 Work it out
That is 6.3.
upper bound = 6.3
So the upper bound of the answer is 6.3.
4 Check
Let's check.
With the rounded numbers we get 6.2.
with the rounded numbers: 9.4 − 3.2 = 6.2
The upper bound, 6.3, is more than that, as it should be.
So the answer is right!
6.3 is more than 6.2
Let's look back.
First: bounds of each number.
Then: choose the bounds.
Then: work it out.
Last: check.
Answer
upper bound = 6.3