A height is 1.65 m to 2 decimal places Step by Step

Step by step

The question

Question: the height is 1.65 m, to 2 decimal places.

Find the upper and lower bounds.

Height: 1.65 m, to 2 decimal places

The real height was rounded.

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

1 Find the step

2 decimal places: we rounded to the nearest 0.01.

So the step is 0.01.

step = 0.01 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 1.65.

Half of 0.01 is 0.005.

half a step = 0.01 ÷ 2 = 0.005 m

3 Find the bounds

The lower bound is 1.65 minus 0.005: 1.645.

lower bound = 1.65 − 0.005 = 1.645 m

Careful!

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

1.64 would round to 1.64, not to 1.65.

Careful: not 1.64 to 1.66 ✗

The upper bound is 1.65 plus 0.005: 1.655.

upper bound = 1.65 + 0.005 = 1.655 m

4 Show it on a number line

So 1.645 ≤ height < 1.655.

This is called the error interval.

1.645 ≤ height < 1.655

5 Check

Let's check.

1.645, rounded to 2 decimal places, is 1.65.

1.645 rounds to 1.65

And 1.654, just under the upper bound, also rounds to 1.65.

So the bounds are right!

1.654 rounds to 1.65

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