Order 0.1666..., 1/5, 0.16 from smallest to largest

Step by step

The question

Question: put 0.166…, 1/5, 0.16 in order, from smallest to largest.

1 Write each as a decimal

To compare, we write every number the same way: as a decimal.

A decimal is tenths, hundredths or thousandths.

5 times 2 is 10.

So we multiply the top and the bottom by 2.

2 tenths is 0.2.

So 1/5 is 0.2.

Careful!

0.166… is not 0.16.

Its 6s go on for ever, so it is a bit more than 0.16.

2 Same number of digits

Zeros at the end of a decimal do not change it: 0.2 is the same as 0.200.

A repeating decimal goes on for ever, so we can write as many of its digits as we need.

So we give every number 3 digits after the point.

3 Compare

Now they all have 3 digits after the point.

So we can forget the point and compare them like whole numbers: 160 < 166 < 200.

4 Write the answer

Now we write the numbers as they were given, in the same order: 0.16, 0.166…, 1/5.

5 Check

Let's check on a number line.

Smaller numbers are further to the left.

We put a dot for each number.

From left to right: 0.16, 0.166…, 1/5.

The same order.

So the answer is right!

Let's look back.

First: write each as a decimal.

Then: same number of digits.

Then: compare.

Then: write the answer.

Last: check.