Find the bounds: 350 people to the nearest 10 Step by Step

Step by step

The question

Question: the number of people is 350, to the nearest 10.

Find the upper and lower bounds.

People: 350 people, to the nearest 10

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 10.

So the step is 10.

step = 10

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 350.

Half of 10 is 5.

half a step = 10 ÷ 2 = 5

3 Find the bounds

The lower bound is 350 minus 5: 345.

lower bound = 350 − 5 = 345

Careful!

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

340 would round to 340, not to 350.

Careful: not 340 to 360 ✗

The upper bound is 350 plus 5: 355.

upper bound = 350 + 5 = 355

4 Show it on a number line

So 345 ≤ people < 355.

This is called the error interval.

345 ≤ people < 355

5 Check

Let's check.

345, rounded to the nearest 10, is 350.

345 rounds to 350

And 354, just under the upper bound, also rounds to 350.

So the bounds are right!

354 rounds to 350

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