Order 5/6, 0.8, 0.85 from smallest to largest

Step by step

The question

Question: put 5/6, 0.8, 0.85 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 6 does not go into 10, 100 or 1000.

So we divide: 5 divided by 6, one digit at a time.

50 divided by 6 is 8, with 2 left.

20 divided by 6 is 3, with 2 left.

2 left again: the 3 repeats for ever.

So 5/6 is 0.833….

Careful!

5/6 is not 0.8.

Its 3s go on for ever, so it is a bit more than 0.8.

2 Same number of digits

Zeros at the end of a decimal do not change it: 0.8 is the same as 0.800.

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: 800 < 833 < 850.

4 Write the answer

Now we write the numbers as they were given, in the same order: 0.8, 5/6, 0.85.

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: 0.8, 5/6, 0.85.

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.