Step by step
The question
Question: the length is 6.4 cm, to 1 decimal place.
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
One decimal place: we rounded to the nearest 0.1.
So the step is 0.1.
2 Half a step
Anything less than half a step away rounds to 6.4.
Half of 0.1 is 0.05.
3 Find the bounds
The lower bound is 6.4 minus 0.05: 6.35.
Careful!
We go only half a step down and half a step up.
6.3 would round to 6.3, not to 6.4.
The upper bound is 6.4 plus 0.05: 6.45.
4 Show it on a number line
On a number line: 6.35, 6.4 in the middle, and 6.45.
6.35 rounds up to 6.4, so it is in: a filled dot.
6.45 would round up, to 6.5.
So it is not in: an open circle.
So 6.35 ≤ length < 6.45.
This is called the error interval.
5 Check
Let's check.
6.35, rounded to 1 decimal place, is 6.4.
And 6.44, just under the upper bound, also rounds to 6.4.
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.