Step by step
The question
Question: the length is 23 cm, to the nearest cm.
Find the upper and lower bounds.
The real length was rounded.
We want the smallest and the biggest it could have been.
1 Find the step
It was rounded to the nearest cm.
So the step is 1 cm.
2 Half a step
Anything less than half a step away rounds to 23.
Half of 1 is 0.5.
3 Find the bounds
The lower bound is 23 minus 0.5: 22.5.
Careful!
We go only half a step down and half a step up.
22 would round to 22, not to 23.
The upper bound is 23 plus 0.5: 23.5.
4 Show it on a number line
So 22.5 ≤ length < 23.5.
This is called the error interval.
5 Check
Let's check.
22.5, rounded to the nearest cm, is 23.
And 23.49, just under the upper bound, also rounds to 23.
So the bounds are right!
Let's look back.
First: find the step.
Then: half a step.
Then: find the bounds.
Then: show it on a number line.
Last: check.