A distance is 70 km to the nearest 10 km Step by Step

Step by step

The question

Question: the distance is 70 km, to the nearest 10 km.

Find the upper and lower bounds.

Distance: 70 km, to the nearest 10 km

The real distance was rounded.

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

1 Find the step

It was rounded to the nearest 10 km.

So the step is 10 km.

step = 10 km

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 70.

Half of 10 is 5.

half a step = 10 ÷ 2 = 5 km

3 Find the bounds

The lower bound is 70 minus 5: 65.

lower bound = 70 − 5 = 65 km

Careful!

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

60 would round to 60, not to 70.

Careful: not 60 to 80 ✗

The upper bound is 70 plus 5: 75.

upper bound = 70 + 5 = 75 km

4 Show it on a number line

So 65 ≤ distance < 75.

This is called the error interval.

65 ≤ distance < 75

5 Check

Let's check.

65, rounded to the nearest 10 km, is 70.

65 rounds to 70

And 74, just under the upper bound, also rounds to 70.

So the bounds are right!

74 rounds to 70

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