Order 2 1/4, 2.3, 2 1/5 from smallest to largest

Step by step

The question

Question: put 2 and 1/4, 2.3, 2 and 1/5 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 1/4 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.

Careful!

The 1 and the 4 are a fraction, not digits after the point.

1/4 is 0.25.

2 and 1/5 means 2 plus 1/5.

5 times 2 is 10, so we multiply the top and the bottom by 2.

1/5 is 2 tenths: 0.2.

So 2 and 1/5 is 2.2.

2 Same number of digits

Zeros at the end of a decimal do not change it: 2.3 is the same as 2.30.

So we give every number 2 digits after the point.

3 Compare

Now they all have 2 digits after the point.

So we can forget the point and compare them like whole numbers: 220 < 225 < 230.

4 Write the answer

Now we write the numbers as they were given, in the same order: 2 and 1/5, 2 and 1/4, 2.3.

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 1/5, 2 and 1/4, 2.3.

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.