text: # 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.
explanation: The document is a lesson on decimal numbers and their representation on number lines. It includes three examples with questions and worked solutions:
  
  1. Example 1: Finding a number 6 units to the right of a plotted point.
  2. Example 2: Plotting 0.332 on a number line.
  3. Example 3: Reading a number from a number line.
  
  Each example contains a question and a detailed solution.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a lesson on decimal numbers and their representation on number lines. It includes three examples with questions and worked solutions:
  
  1. Example 1: Finding a number 6 units to the right of a plotted point.
  2. Example 2: Plotting 0.332 on a number line.
  3. Example 3: Reading a number from a number line.
  
  Each example contains a question and a detailed solution.
  
  Label: multiple-question-and-answer