# 6.03 Decimal numbers on number line

Lesson

## Are you ready?

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.

Loading video...

### 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.

Loading video...

### 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.
The text passage contains multiple examples and explanations on how to plot and read decimal numbers, specifically thousandths, on a number line. Each example includes a worked solution and sometimes a calculation.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 6.03 Decimal numbers on number line

Lesson

## Are you ready?

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.

Loading video...

### 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.

Loading video...

### 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.
user
The text passage contains multiple examples and explanations on how to plot and read decimal numbers, specifically thousandths, on a number line. Each example includes a worked solution and sometimes a calculation.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS