Step by step
The question
Question: compare 1/3 and 0.3.
1 Write it 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: 0.3 is the same as 0.300.
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 both have 3 digits after the point.
So we can forget the point and compare them like whole numbers: 300 < 333.
4 Write the answer
Now with the numbers as they were given: 1/3 > 0.3.
1/3 is greater than 0.3.
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.
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.