Compare 7/8 and 0.9

Step by step

The question

Question: compare 7/8 and 0.9.

1 Write it as a decimal

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

A decimal is tenths, hundredths or thousandths.

8 times 125 is 1000.

So we multiply the top and the bottom by 125.

875 thousandths is 0.875.

So 7/8 is 0.875.

2 Same number of digits

Zeros at the end of a decimal do not change it: 0.9 is the same as 0.900.

So we give every number 3 digits after the point.

3 Compare

Now both have 3 digits after the point.

So we can forget the point and compare them like whole numbers: 875 < 900.

Careful!

More digits does not mean bigger.

Compare 0.875 with 0.900.

4 Write the answer

Now with the numbers as they were given: 7/8 < 0.9.

7/8 is less than 0.9.

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: 7/8, 0.9.

The same order.

So the answer is right!

Let's look back.

First: write it as a decimal.

Then: same number of digits.

Then: compare.

Then: write the answer.

Last: check.