Which is bigger, 2 1/4 or 2.2

Step by step

The question

Question: which is bigger, 2 and 1/4 or 2.2?

1 Write it 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 Same number of digits

Zeros at the end of a decimal do not change it: 2.2 is the same as 2.20.

So we give every number 2 digits after the point.

3 Compare

Now both have 2 digits after the point.

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

4 Write the answer

Now with the numbers as they were given: 2.2 < 2 and 1/4.

So 2 and 1/4 is bigger.

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: 2.2, 2 and 1/4.

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.