Step by step
The question
Question: put 2 and 1/3, 2.3, 2 and 1/4, 2.33 in order, from smallest to largest.
1 Write each as a decimal
To compare, we write every number the same way: as a decimal.
2 and 1/3 means 2 plus 1/3.
For 1/3 we divide.
10 divided by 3 is 3, with 1 left.
1 left again: the 3 repeats for ever.
So 2 and 1/3 is 2.333….
Careful!
The 1 and the 3 are a fraction, not digits after the point.
1/3 is 0.333….
2 and 1/4 means 2 plus 1/4.
4 times 25 is 100, so we multiply the top and the bottom by 25.
1/4 is 25 hundredths: 0.25.
So 2 and 1/4 is 2.25.
2 Same number of digits
Zeros at the end of a decimal do not change it: 2.3 is the same as 2.300.
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 they all have 3 digits after the point.
So we can forget the point and compare them like whole numbers: 2250 < 2300 < 2330 < 2333.
4 Write the answer
Now we write the numbers as they were given, in the same order: 2 and 1/4, 2.3, 2.33, 2 and 1/3.
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: 2 and 1/4, 2.3, 2.33, 2 and 1/3.
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.