Step by step
The question
Question: x = 8.6 and y = 2.1, both to 1 decimal place.
Find the lower bound of x − y.
1 Bounds of each number
The number x is 8.6, to 1 decimal place.
Half a step is 0.05.
So it is from 8.55 up to 8.65.
8.55 ≤ x < 8.65
8.6 ± 0.05
The number y is 2.1, to 1 decimal place.
Half a step is 0.05.
So it is from 2.05 up to 2.15.
2.05 ≤ y < 2.15
2.1 ± 0.05
2 Choose the bounds
Taking away a smaller number leaves more.
So the smallest answer is the smallest x minus the biggest y.
So we use 8.55 and 2.15.
lower bound = 8.55 − 2.15
smallest: smallest − biggest
Careful!
Taking away a smaller number makes the answer bigger.
Careful: not 8.55 − 2.05 ✗
3 Work it out
That is 6.4.
lower bound = 6.4
So the lower bound of the answer is 6.4.
4 Check
Let's check.
With the rounded numbers we get 6.5.
with the rounded numbers: 8.6 − 2.1 = 6.5
The lower bound, 6.4, is less than that, as it should be.
So the answer is right!
6.4 is less than 6.5
Let's look back.
First: bounds of each number.
Then: choose the bounds.
Then: work it out.
Last: check.
Answer
lower bound = 6.4