Step by step
The question
Question: the mass is 6 kg, to the nearest kg.
Find the upper and lower bounds.
Mass: 6 kg, to the nearest kg
The real mass was rounded.
We want the smallest and the biggest it could have been.
1 Find the step
It was rounded to the nearest kg.
So the step is 1 kg.
step = 1 kg
upper bound = the biggest it could be
lower bound = the smallest it could be
2 Half a step
Anything less than half a step away rounds to 6.
Half of 1 is 0.5.
half a step = 1 ÷ 2 = 0.5 kg
3 Find the bounds
The lower bound is 6 minus 0.5: 5.5.
lower bound = 6 − 0.5 = 5.5 kg
Careful!
We go only half a step down and half a step up.
5 would round to 5, not to 6.
Careful: not 5 to 7 ✗
The upper bound is 6 plus 0.5: 6.5.
upper bound = 6 + 0.5 = 6.5 kg
4 Show it on a number line
So 5.5 ≤ mass < 6.5.
This is called the error interval.
5.5 ≤ mass < 6.5
5 Check
Let's check.
5.5, rounded to the nearest kg, is 6.
5.5 rounds to 6
And 6.49, just under the upper bound, also rounds to 6.
So the bounds are right!
6.49 rounds to 6
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.
Answer
5.5 ≤ mass < 6.5