Step by step
The question
Question: the distance is 18.0 km, to 1 decimal place.
Find the upper and lower bounds.
The real distance was rounded.
We want the smallest and the biggest it could have been.
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 18.0.
Half of 0.1 is 0.05.
3 Find the bounds
The lower bound is 18.0 minus 0.05: 17.95.
Careful!
We go only half a step down and half a step up.
17.9 would round to 17.9, not to 18.0.
The upper bound is 18.0 plus 0.05: 18.05.
4 Show it on a number line
So 17.95 ≤ distance < 18.05.
This is called the error interval.
5 Check
Let's check.
17.95, rounded to 1 decimal place, is 18.0.
And 18.04, just under the upper bound, also rounds to 18.0.
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.