A length is 5000 m to the nearest 100 m Step by Step

Step by step

The question

Question: the length is 5000 m, to the nearest 100 m.

Find the upper and lower bounds.

Length: 5000 m, to the nearest 100 m

The real length was rounded.

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

1 Find the step

It was rounded to the nearest 100 m.

So the step is 100 m.

step = 100 m

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 5000.

Half of 100 is 50.

half a step = 100 ÷ 2 = 50 m

3 Find the bounds

The lower bound is 5000 minus 50: 4950.

lower bound = 5000 − 50 = 4950 m

Careful!

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

4900 would round to 4900, not to 5000.

Careful: not 4900 to 5100 ✗

The upper bound is 5000 plus 50: 5050.

upper bound = 5000 + 50 = 5050 m

4 Show it on a number line

So 4950 ≤ length < 5050.

This is called the error interval.

4950 ≤ length < 5050

5 Check

Let's check.

4950, rounded to the nearest 100 m, is 5000.

4950 rounds to 5000

And 5049, just under the upper bound, also rounds to 5000.

So the bounds are right!

5049 rounds to 5000

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