# 5.03 Decimal numbers on number line

Lesson

## Ideas

We have previously looked at  how to plot decimals on a number line.  Let's practice.

### Examples

#### Example 1

What number is shown on the following number line?

Worked Solution
Create a strategy

The line between 0.5 and 0.6 has been divided into 10 spaces, so each space in the number line is equal to \dfrac{1}{100} or 0.01.

Apply the idea

The point is plotted 5 spaces up from 0.5. 5 lots of 0.01 is 0.05.

So we need to add 0.05 to 0.5. We can use a place value table to add them.

So the number in the number line is 0.55.

Idea summary

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

## Plot thousandths on the number line

We can zoom in and divide \dfrac{1}{100} into 10 equal pieces to show \dfrac{10}{1000}, which we can then use to plot thousandths.

This video shows us how.

### Examples

#### Example 2

Plot 0.332 on the number line.

Worked Solution
Create a strategy

There are 10 spaces between 0.33 and 0.34, so each space on the number line is equal to \dfrac{1}{1000} or 1 thousandth.

Apply the idea

0.332 has 2 thousandths. To plot 0.332\, we need to move 2\, spaces to the right of 0.33.

Idea summary

To plot a decimal with thousandths, we can plot the hundredth before and after the decimal and divide the line between them into 10 spaces, where each space represents a thousandth.

From the smaller hundredth, we can count to the right how many thousandths there are in the decimal.

## Read thousandths on a number line

This video shows how to read numbers off of a number line for numbers in the thousandths.

### Examples

#### Example 3

What number is shown on the following number line?

Worked Solution
Create a strategy

Since there are 10 spaces between 0 and 0.01, each space on the number line is equal to 1 thousandth or 0.001.

Apply the idea

The point is 1 space after 0.015. So we need to add 1 thousandths, or 0.001, to 0.015.

We can use a vertical algorithm: \begin{array}{c}& &0 &. &0 &1 & 5 \\ &+ &0 &. &0 &0 &1 \\ \hline & &0 &. &0 &1 &6 \\ \hline \end{array}

So the the number on the number line is: 0.016

Idea summary

10 hundredths make 1 tenth.

10 thousandths make 1 hundredth.

### Outcomes

#### MA3-7NA

compares, orders and calculates with fractions, decimals and percentages