Step by step
The question
Question: compare 2/3 and 0.6.
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: 2 divided by 3, one digit at a time.
20 divided by 3 is 6, with 2 left.
2 left again: the 6 repeats for ever.
So 2/3 is 0.666….
Careful!
2/3 is not 0.6.
Its 6s go on for ever, so it is a bit more than 0.6.
2 Same number of digits
Zeros at the end of a decimal do not change it: 0.6 is the same as 0.600.
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: 600 < 666.
4 Write the answer
Now with the numbers as they were given: 2/3 > 0.6.
2/3 is greater than 0.6.
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: 0.6, 2/3.
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.