Order 0.35, 1/3, 0.3 from smallest to largest

Step by step

The question

Question: put 0.35, 1/3, 0.3 in order, from smallest to largest.

1 Write each as a decimal

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

The bottom 3 does not go into 10, 100 or 1000.

So we divide: 1 divided by 3, one digit at a time.

10 divided by 3 is 3, with 1 left.

1 left again: the 3 repeats for ever.

So 1/3 is 0.333….

Careful!

1/3 is not 0.3.

Its 3s go on for ever, so it is a bit more than 0.3.

2 Same number of digits

Zeros at the end of a decimal do not change it: 0.35 is the same as 0.350.

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: 300 < 333 < 350.

4 Write the answer

Now we write the numbers as they were given, in the same order: 0.3, 1/3, 0.35.

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: 0.3, 1/3, 0.35.

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.