# 6.03 Decimal numbers on number line

Lesson

## Ideas

We have  plotted whole numbers on number lines  before. This skill will help with plotting decimal numbers.

### Examples

#### Example 1

A point is plotted on the number line. Find the number that is 6 units to the right of this plotted point.

Worked Solution
Create a strategy

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

Apply the idea

Starting at the plotted point jump 6 spaces to the right.

We can see on the number line, that we are 1 space below 10, so we are at the number 9.

Idea summary

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

## Plot thousandths on number lines

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 number on the number line is: 0.016

Idea summary

10 hundredths make 1 tenth.

10 thousandths make 1 hundredth.

Decimals and fractions are just different ways to express the same number.