Step by step
The question
Question: the length is 24 cm, to the nearest cm.
Find the upper and lower bounds.
The real length was rounded.
The upper bound is the biggest it could have been.
The lower bound is the smallest.
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 24.
Half of 1 is 0.5.
3 Find the bounds
The lower bound is 24 minus 0.5: 23.5.
Careful!
We go only half a step down and half a step up.
23 would round to 23, not to 24.
The upper bound is 24 plus 0.5: 24.5.
4 Show it on a number line
On a number line: 23.5, 24 in the middle, and 24.5.
23.5 rounds up to 24, so it is in: a filled dot.
24.5 would round up, to 25.
So it is not in: an open circle.
So 23.5 ≤ length < 24.5.
This is called the error interval.
5 Check
Let's check.
23.5, rounded to the nearest cm, is 24.
And 24.49, just under the upper bound, also rounds to 24.
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.