Find the bounds: 1200 people to the nearest 100 Step by Step

Step by step

The question

Question: the number of people is 1200, to the nearest 100.

Find the upper and lower bounds.

People: 1200 people, to the nearest 100

The real number was rounded.

We want the smallest and the biggest it could have been.

1 Find the step

It was rounded to the nearest 100.

So the step is 100.

step = 100

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 1200.

Half of 100 is 50.

half a step = 100 ÷ 2 = 50

3 Find the bounds

The lower bound is 1200 minus 50: 1150.

lower bound = 1200 − 50 = 1150

Careful!

We go only half a step down and half a step up.

1100 would round to 1100, not to 1200.

Careful: not 1100 to 1300 ✗

The upper bound is 1200 plus 50: 1250.

upper bound = 1200 + 50 = 1250

4 Show it on a number line

So 1150 ≤ people < 1250.

This is called the error interval.

1150 ≤ people < 1250

5 Check

Let's check.

1150, rounded to the nearest 100, is 1200.

1150 rounds to 1200

And 1249, just under the upper bound, also rounds to 1200.

So the bounds are right!

1249 rounds to 1200

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