Step by step
The question
Question: the length is 36 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 36.
Half of 1 is 0.5.
3 Find the bounds
The lower bound is 36 minus 0.5: 35.5.
Careful!
We go only half a step down and half a step up.
35 would round to 35, not to 36.
The upper bound is 36 plus 0.5: 36.5.
4 Show it on a number line
On a number line: 35.5, 36 in the middle, and 36.5.
35.5 rounds up to 36, so it is in: a filled dot.
36.5 would round up, to 37.
So it is not in: an open circle.
So 35.5 ≤ length < 36.5.
This is called the error interval.
5 Check
Let's check.
35.5, rounded to the nearest cm, is 36.
And 36.49, just under the upper bound, also rounds to 36.
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.