GCSE Maths Number FDP Decimals

Decimal Number Line

Decimal Number Line

Here we will learn about decimal number lines, including what decimal number lines are and how to use them.

There are also decimal number line worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is a decimal number line?

A decimal number line is a number line that can help us to visualise decimal numbers. Decimal numbers are parts of whole numbers and have digits after a decimal point.

Decimals are numbers that have parts that are not whole. Our number system splits whole numbers into tenths, hundredths, thousandths, and so on.

For example, this number line goes from zero to one in steps of 0.1.

Decimal Number Line image 1

Below, the number \bf{0.638} has been marked on a decimal number line. Its position has been estimated between 0.6 and 0.7, but closer to 0.6.

Decimal Number Line image 2

If we zoom in and consider a number line between 0.6 and 0.7 that goes up in steps of 0.01 then we can position the decimal \bf{0.638} more accurately. This time the position has been estimated between 0.63 and 0.64, but closer to 0.64.

Decimal Number Line image 3

If we zoom in once more and consider a number line between 0.63 and 0.64 that goes up in steps of 0.001 then we can mark the decimal \bf{0.638} in its exact position.

Decimal Number Line image 4

Decimal number lines can use hundredths or thousandths. The scale can be split up into different equal parts (or increments).

For example, this decimal number line has been split up into fifths that go up in steps of 0.2.

Decimal Number Line image 5

This decimal number line has been split up into halves that go up in steps of 0.5.

Decimal Number Line image 6

This decimal number line has been split up into quarters that go up in steps of 0.25.

Decimal number lines can also be used to represent negative numbers.

For example,

Decimal Number Line image 8

What is a decimal number line?

What is a decimal number line?

How to fill in values on a decimal number line

In order to fill in values on a decimal number line:

  1. Consider the top and bottom of the scale and the number of intervals.
  2. Calculate the length of each interval step by finding the difference in the top and bottom of the scale and dividing by the number of intervals.
  3. Fill in the missing values.

Explain how to fill in values on a decimal number line

Explain how to fill in values on a decimal number line

Decimals worksheet (includes decimal number line)

Decimals worksheet (includes decimal number line)

Decimals worksheet (includes decimal number line)

Get your free decimal number line worksheet of 20+ decimals questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE
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Decimals worksheet (includes decimal number line)

Decimals worksheet (includes decimal number line)

Decimals worksheet (includes decimal number line)

Get your free decimal number line worksheet of 20+ decimals questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Decimal number line examples

Example 1: fill in the scale

Fill in the scale.

Decimal Number Line Example 1

  1. Consider the bottom and top of the scale and the number of intervals.

The bottom of the scale is 7, the top of the scale is 8 and there are 5 intervals.

2Calculate the length of each interval step by finding the difference in the top and bottom of the scale and dividing by the number of intervals.

To calculate the length of an interval step we can use the formula

(\text{Top of the scale} - \text{bottom of the scale}) \div \text{number of intervals}.

This gives,

(8-7)\div 5=0.2.

So the scale goes up in steps of 0.2.

3Fill in the missing values.

Start from the bottom of the scale, 7, and go up the scale, adding on 0.2 each time.

Decimal Number Line Example 1 Step 3

Example 2: fill in the scale

Fill in the scale.

Decimal Number Line Example 2

The bottom of the scale is 5, the top of the scale is 9 and there are 8 intervals.

To calculate the length of an interval step we can use the formula


(\text{Top of the scale} - \text{bottom of the scale}) \div \text{number of intervals}.


This gives,


(9-5) \div 8=0.5.


So the scale goes up in steps of 0.5.

Start from the bottom of the scale, 5 and go up the scale, adding on 0.5 each time.


Decimal Number Line Example 2 Step 3

Example 3: fill in the scale

Fill in the scale.

Decimal Number Line Example 3

The bottom of the scale is 12, the top of the scale is 14 and there are 5 intervals.

To calculate the length of an interval step we can use the formula


(\text{Top of the scale} - \text{bottom of the scale}) \div \text{number of intervals}.


This gives,


(14-12)\div 5=0.4.


So the scale goes up in steps of 0.4.

Start from the bottom of the scale, 12 and go up the scale, adding on 0.4 each time.


Decimal Number Line Example 3 Step 3

Example 4: finding a missing value

Find the missing value.

Decimal Number Line Example 4

The bottom of the scale is 5.2, the top of the scale is 6.0 and there are 8 intervals.

To calculate the length of an interval step we can use the formula


(\text{Top of the scale} - \text{bottom of the scale}) \div \text{number of intervals}.


This gives,


(6.0-5.2)\div 8=0.1.


So the scale goes up in steps of 0.1.

We need the 4th value. So we can multiply the interval step by 5 and add it to the bottom of the scale,


5.2+(4\times 0.1)=5.6.


Decimal Number Line Example 4 Step 3


You can always fill in other values on the scale to double check.

Example 5: finding a missing value

Find the missing value.

Decimal Number Line Example 5

The bottom of the scale is 14, the top of the scale is 17 and there are 6 intervals.

To calculate the length of an interval step we can use the formula


(\text{Top of the scale} - \text{bottom of the scale}) \div \text{number of intervals}.


This gives,


(17-14)\div 6=0.5.


So the scale goes up in steps of 0.5.

We need the 5th value. So we can multiply the interval step by 5 and add it to the bottom of the scale,


14+(5\times 0.5)=16.5.


Decimal Number Line Example 5 Step 3


You can always fill in other values on the scale to double check.

Example 6: finding a missing value

Find the missing value.

Decimal Number Line Example 6

The bottom of the scale is 7.1, the top of the scale is 7.5 and there are 8 intervals.

To calculate the length of an interval step we can use the formula


(\text{Top of the scale} - \text{bottom of the scale}) \div \text{number of intervals}.


This gives,


(7.5-7.1)\div 8=0.05.


So the scale goes up in steps of 0.05.

We need the 7th value. So we can multiply the interval step by 7 and add it to the bottom of the scale,


7.1+(7\times 0.05)=7.45.


Decimal Number Line Example 6 step 3


You can always fill in other values on the scale to double check.

Common misconceptions

  • Assuming a decimal number line goes up in tenths

It is worth double checking what the intervals in a number line are. It is easy to assume it will be tenths, but often steps of 0.2 are used. This is a useful tip when reading scales on graphs.

Practice decimal number line questions

1. Find the missing value.

 

Decimal Number Line Practice Question 1

6.4
GCSE Quiz True

6.1
GCSE Quiz False

6.5
GCSE Quiz False

6.2
GCSE Quiz False

The bottom of the scale is 6, the top of the scale is 7 and there are 5 intervals.

 

To calculate the length of an interval step we can use the formula

 

(\text{Top of the scale}-\text{bottom of the scale}) \div \text{number of intervals}.

 

This gives,

 

(7-6)\div 5=0.2.

 

We need the 2nd value, so we can multiply the interval step by 2 and add it to the bottom number.

 

6+(2\times 0.2)=6.4

 

The missing value is 6.4.

2. Find the missing value.

 

Decimal Number Line Practice Question 2

2.12
GCSE Quiz False

2.3
GCSE Quiz True

2.2
GCSE Quiz False

2.35
GCSE Quiz False

The bottom of the scale is 2.1, top of the scale is 2.7 and there are 6 intervals.

 

To calculate the length of an interval step we can use the formula

 

(\text{Top of the scale}-\text{bottom of the scale}) \div \text{number of intervals}.

 

This gives,

 

(2.7-2.1)\div 6=0.1.

 

We need the 2nd value, so we can multiply the interval step by 2 and add it to the bottom number.

 

2.1+(2\times 0.1)=2.3

 

So the missing value is 2.3.

3. Find the missing value.

 

Decimal Number Line Practice Question 3

5.26
GCSE Quiz False

5.5
GCSE Quiz False

5.25
GCSE Quiz True

5.7
GCSE Quiz False

The bottom of the scale is 5.2, the top of the scale is 5.3 and there are 10 intervals.

 

To calculate the length of an interval step we can use the formula

 

(\text{Top of the scale}-\text{bottom of the scale}) \div \text{number of intervals}.

 

This gives,

 

(5.3-5.2)\div 10=0.01.

 

We need the 5th value, so we can multiply the interval step by 5 and add it to the bottom number.

 

5.2+(5\times 0.01)=5.25

 

The missing value is 5.25.

4. Find the missing value.

 

Decimal Number Line Practice Question 4

16.6
GCSE Quiz False

17.5
GCSE Quiz False

17.8
GCSE Quiz True

16.8
GCSE Quiz False

The bottom of the scale is 16.2, the top of the scale is 18.2 and there are 5 intervals.

 

To calculate the length of an interval step we can use the formula

 

(\text{Top of the scale}-\text{bottom of the scale}) \div \text{number of intervals}.

 

This gives,

 

(18.2-16.2)\div 5=0.4.

 

We need the 4th value, so we can multiply the interval step by 4 and add it to the bottom number.

 

16.2+(4\times 0.4)=17.8

 

The missing value is 17.8.

5. Find the missing value.

 

Decimal Number Line Practice Question 5

7.25
GCSE Quiz True

6.8
GCSE Quiz False

8.3
GCSE Quiz False

7.5
GCSE Quiz False

The bottom of the scale is 6.5, the top of the scale is 9.0 and there are 10 intervals.

 

To calculate the length of an interval step we can use the formula

 

(\text{Top of the scale}-\text{bottom of the scale}) \div \text{number of intervals}.

 

This gives,

 

(9.0-6.5)\div 10=0.25.

 

We need the 3rd value, so we can multiply the interval step by 3 and add it to the bottom number.

 

6.5+(3\times 0.25)=7.25

 

The missing value is 7.25.

6. Find the missing value.

 

Decimal Number Line Practice Question 6

5.8
GCSE Quiz False

7.1
GCSE Quiz False

6.4
GCSE Quiz True

6.5
GCSE Quiz False

The bottom of the scale is 5.5, the top of the scale is 7.3 and there are 6 intervals.

 

To calculate the length of an interval step we can use the formula

 

(\text{Top of the scale}-\text{bottom of the scale}) \div \text{number of intervals}.

 

This gives,

 

(7.3-5.5)\div 6=0.3.

 

We need the 3rd value, so we can multiply the interval step by 3 and add it to the bottom number.

 

5.5+(3\times 0.3)=6.4

 

The missing value is 6.4.

Decimal number line GCSE questions

1.

Decimal Number Line GCSE Question 1

(a) Find the number 1.7 on the number line.

Mark it with a cross (X).

 

 

Decimal Number Line GCSE Question 1a image 2

(b) Find the number 0.13 on the number line.

Mark it with a cross (X).

 

(2 marks)

Show answer

(a)

 

Decimal Number Line GCSE Question 1a image 1

(1)

 

(b)

 

Decimal Number Line GCSE Question 1b image 1

(1)

2.

Decimal Number Line GCSE Question 2

(a) Write down the number marked by the arrow.

 

Decimal Number Line GCSE Question 2a image 1

(b) Write down the number marked by the arrow.

 

Decimal Number Line GCSE Question 2c image 1

(c) Write down the number marked by the arrow.

 

(3 marks)

Show answer

(a) 3.8

(1)

 

(b) 5.74

(1)

 

(c) 2.366

(1)

3.

Decimal Number Line GCSE Question 3

(a) Write down the number marked by the arrow

 

Decimal Number Line GCSE Question 3a

(b) Write down the number marked by the arrow.

 

Decimal Number Line GCSE Question 3c

(c) Write down the number marked by the arrow.

 

(3 marks)

Show answer

(a) 13.8

(1)

 

(b) 0.55

(1)

 

(c) 1.675

(1)

4. Amir says that the number the arrow is pointing to is 0.34.

 

Liam says that the number the arrow is pointing to is 0.38.

 

Decimal Number Line GCSE Question 4

 

Who is correct? Explain your answer.

 

(2 marks)

Show answer

Liam

(1)

 

Correct explanation

(1)

For example, Amir thinks the scale goes up in steps of 0.01.

The scale goes up in steps of 0.02, so the correct answer is 0.38.

Learning checklist

You have now learned how to:

  • Understand and use decimal number lines

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FREE GCSE maths practice papers (Edexcel, AQA & OCR)

8 sets of free exam practice papers written by maths teachers and examiners for Edexcel, AQA and OCR.

Each set of exam papers contains the three papers that your students will expect to find in their GCSE mathematics exam.

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