# 6.03 Decimals on a number line

Lesson

## Ideas

Remember when we used a  number line to order whole numbers  ? Let's practice.

### Examples

#### Example 1

Plot the following numbers on the number lines:

a

Plot 3 on the number line below.

Worked Solution
Create a strategy

Use the fact that each space on the number line represents an increase of 1 unit.

Apply the idea

To plot 3, we can start at zero and jump right 3 spaces.

b

Plot 528 on the number line below.

Worked Solution
Create a strategy

Use the fact that each space on the number line represents an increase of 1 unit.

Apply the idea

528 is 3 more than 525.

To plot 528 we can start at 525 and jump right 3 spaces.

c

Plot 700 on the number line below.

Worked Solution
Create a strategy

Use the fact that each space on the number line represents an increase of 100 units.

Apply the idea

700 is 200 more than 500.

To plot 700 we can start at 500 and jump right 2 spaces.

Idea summary

To plot a number on a number line we must consider how many units each space between ticks represents.

## Number lines with tenths

When we divide 1 unit into 10 equal pieces, it is broken into 10 tenths, as shown below.

This video looks at how to plot and read tenths on a number line.

### Examples

#### Example 2

Plot 0.3 on the number line.

Worked Solution
Create a strategy

The number line is divided into 10 spaces between 0 and 1. So each space represents 1 tenth.

Apply the idea

We need to move 3 tenths spaces from 0 to plot 0.3. So we jump to the right 3 spaces.

Idea summary

When we divide 1 unit into 10 equal pieces, it is broken into 10 tenths.

## Number lines with hundredths

When we divide 1 unit into 100 equal pieces we end up with hundredths. We can also get the size of 1 hundredth by dividing 1 tenth up into 10 equal pieces, as shown below.

This video looks at how to plot and read hundredths off a number line.

### Examples

#### Example 3

What number is shown on the following number line?

Worked Solution
Create a strategy

Count the number of spaces starting from 0 up to the point.

Apply the idea

The number line between 0 and 0.1 has been divided into 10 spaces, so each space represents a hundredth or 0.01.

The point is 7 spaces from 0. So, 7 \times 0.01 is 0.07.

The number shown on the number line is 0.07.

Idea summary

10 hundredths make 1 tenth. The larger the number, the further to the right it will be on a number line.

### Outcomes

#### VCMNA159

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation