# 5.05 Compare decimal numbers

Lesson

## Are you ready?

Remembering how to compare whole numbers is going to help us compare decimals in this lesson. Let's try this practice problem to review.

### Examples

#### Example 1

Which symbol, greater than (\gt) or less than (\lt) will make the following statements true?

a

91 \, ⬚ \, 97

A
\gt
B
\lt
Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea

As we can see in the table, both numbers in the tens column have the same number so we move to the units column.

In the units column, we can see that 1 is smaller than 7.

So the correct answer is 91 \lt 97, option B.

b

682 \, ⬚ \, 782

A
\gt
B
\lt
Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea

In the hundreds column, we can see that 6 is smaller than 7. We do not need to compare the remaining columns since we already know which is greater.

So the correct answer is 682 \lt 782, option B.

Idea summary

\gt means "greater than".

\lt means "less than".

## Compare decimals with thousandths

We can use place value columns to help us compare numbers with decimals. If we have 0.342, and we are comparing it to 0.458, we know that 342 is smaller than 458, so 342 thousandths is smaller than 458 thousandths. In this video we work through some examples, and see how we can compare decimals.

### Examples

#### Example 2

Fill in the box the greater than (\gt) or less than (\lt) symbol that would make this number sentence true. 0.082 \, ⬚ \, 0.088

Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea

Write the decimals in a place value table and use zeros as place holders.

As we can see in the table, both numbers in the units, tenths, and hundredths columns have the same number so we move to the thousandths column.

In the thousandths column, we can see that 2 is smaller than 8.

We can write the number sentence as:0.082 \lt 0.088

Idea summary

We can use a place value table to compare decimals.

## Compare numbers beyond thousandths

This video shows how to compare numbers that have many decimal places.

### Examples

#### Example 3

Fill in the box the greater than (\gt) or less than (\lt) symbol that would make this number sentence true. 0.754 \, ⬚ \, 0.6094

Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea

Write the decimals in a place value table and use zeros as place holders.

In the tenths column, we can see that 7 is larger than 6. We do not need to compare the remaining columns since we already know which is larger.

We can write the number sentence as:0.754 \gt 0.6094

Idea summary

When using a place value table to compare decimals we can start at the place value column furthest to the left and work to the right, comparing the values in each column to work out the bigger/smaller number.

Or, we can add zeros at the end of a decimal so we can compare the same number of place value columns. For example, if we wanted to compare 0.45 and 0.672, we could write 0.45 as 0.450. This means we can compare thousandths to thousandths.

### Outcomes

#### MA3-7NA

compares, orders and calculates with fractions, decimals and percentages