Which is bigger, 2 1/4 or 2.2 Easy

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.

▶ Watch it solved

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

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.

▶ Watch it solved

Order 0.333..., 0.3, 1/4, 2/3 from smallest to largest Harder

The question

Question: put 0.333…, 0.3, 1/4, 2/3 in order, from smallest to largest.

1 Write each as a decimal

To compare, we write every number the same way: as a decimal.

A decimal is tenths, hundredths or thousandths.

4 times 25 is 100.

So we multiply the top and the bottom by 25.

25 hundredths is 0.25.

So 1/4 is 0.25.

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!

0.333… 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 they all have 3 digits after the point.

So we can forget the point and compare them like whole numbers: 250 < 300 < 333 < 666.

4 Write the answer

Now we write the numbers as they were given, in the same order: 1/4, 0.3, 0.333…, 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: 1/4, 0.3, 0.333…, 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.

▶ Watch it solved