## What you need to know

Things to remember:

• To compare numbers, we look at the highest place value first, and then move to the right until we find numbers that are different.
• A smaller value means a smaller number.
• A bigger value means a bigger number.

Let’s look back at how we compare whole numbers. How would we decide which is smaller out of 5674 and 5655? We start by comparing the value of the thousands and work from left to right until we find numbers that are different.

$$5\rightarrow Thousands$$

$$5\rightarrow Thousands$$

Both numbers have the same thousands, so we need to move onto the hundreds.

$$6\rightarrow Hundreds$$

$$6\rightarrow Hundreds$$

The hundreds are the same as well, so now we need to move onto the tens.

$$7\rightarrow Tens$$

$$5\rightarrow Tens$$

Now that we have numbers that are different, we can look for the smaller number. The smaller number is 5, so 5655 is smaller than 5674.

We can do the same with decimals numbers.

Which is bigger, 23.45 or 23.48?

We start by comparing the tens, and work through until we find a difference.

$$2\rightarrow Tens$$

$$2\rightarrow Tens$$

Both numbers have the same tens, so we need to move onto the units.

$$3\rightarrow Units$$

$$3\rightarrow Units$$

The units are the same as well, so now we need to move onto the tenths.

$$4\rightarrow Tenths$$

$$4\rightarrow Tenths$$

The tenths are also the same, so we have to move onto the hundredths.

$$5\rightarrow Hundredths$$

$$8\rightarrow Hundredths$$

We have a difference! We are looking for the bigger number and know that 8 is bigger than 5, so 23.48 must be bigger than 23.45.

We do the same when looking for the smallest number.

Which is smaller, 55.67 or 55.37?

We start by comparing the tens, and work through until we find a difference.

$$5\rightarrow Tens$$

$$5\rightarrow Tens$$

Both numbers have the same tens, so we need to move onto the units.

$$5\rightarrow Units$$

$$5\rightarrow Units$$

The units are the same as well, so now we need to move onto the tenths.

$$6\rightarrow Tenths$$

$$3\rightarrow Tenths$$

We have a difference! We are looking for the smaller number and know that 3 is smaller than 6, so 55.37 must be smaller than 55.67.

## Example Questions

We don’t have any tens here, so we will start by comparing the units.

$$9\rightarrow Units$$

$$9\rightarrow Units$$

The units are the same as well, so now we need to move onto the tenths.

$$1\rightarrow Tenths$$

$$1\rightarrow Tenths$$

The tenths are also the same, so we have to move onto the hundredths.

$$4\rightarrow Hundredths$$

$$8\rightarrow Hundredths$$

We have a difference! We are looking for the smaller number and know that 4 is smaller than 8, so 9.14 must be smaller than 9.18.

We start by comparing the tens, and work through until we find a difference.

$$1\rightarrow Tens$$

$$1\rightarrow Tens$$

Both numbers have the same tens, so we need to move onto the units.

$$2\rightarrow Units$$

$$2\rightarrow Units$$

The units are the same as well, so now we need to move onto the tenths.

$$5\rightarrow Tenths$$

$$7\rightarrow Tenths$$

We have a difference! We are looking for the bigger number and know that 7 is bigger than 5, so 12.76 must be bigger than 12.56.