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Place value

Decimal placesMultiplying and dividing by powers of 10

Simplifying fractions

This topic is relevant for:

Here we will learn about converting **decimals to fractions**.

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

Converting **decimals to fractions **is representing a decimal as a fraction without changing its value.

E.g.

\[0.25=\frac{1}{4}\]

\[0.125=\frac{1}{8}\]

\[0.2857142857…=\frac{2}{7}\]

\[ 3.2=3 \frac{1}{5}\]

*Note: The decimals being converted in this page are terminating decimals, which means the decimal stops and does not have an infinite number of decimal places. We can also convert recurring decimals to fraction** s*.

In order to convert from a terminating decimal to a fraction you need to:

**Write the decimal as a fraction by dividing by**1 (this will make the denominator1 )**Convert the numerator to an integer by multiplying by a multiple of**10 , e.g.10, 100, 1000 . You need to do the same to the denominator to create an equivalent fraction**Simplify the fraction where possible****Clearly state the answer showing the ‘decimal’ = ‘fraction’**

Get your free decimals to fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONGet your free decimals to fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONConvert

**Write the decimal as a fraction by dividing by**1

\[0.3\div1\]

\[\frac{0.3}{1}\]

**2Convert the numerator to an integer (by multiplying by a multiple of 10). You need to do the same to the denominator to create an equivalent fraction**

The lowest value in the number

This means if we multiply

If you multiplied the numerator by

\[\frac{0.3}{1}\]

\[\frac{0.3\times10}{1\times10}\]

\[\frac{3}{10}\]

3**Simplify the fraction if possible**

\frac{3}{10} cannot be simplified as

4**Clearly state the answer showing the ‘decimal’ = ‘fraction’**

\[0.3=\frac{3}{10}\]

Convert

**Write the decimal as a fraction by dividing by 1**

\[0.22\div1\]

\[\frac{0.22}{1}\]

**Convert the numerator to an integer (by multiplying by a multiple of 10). You need to do the same to the denominator to create an equivalent fraction**

The lowest value in the number

This means if we multiply

If you only multiplied the numerator by

\[\frac{0.22}{1}\]

\[\frac{0.22\times100}{1\times100}\]

\[\frac{22}{100}\]

**Simplify the fraction if possible**

\frac{22}{100} can be simplified by dividing the numerator and denominator by

\[\frac{22\div2}{100\div2}\]

\[\frac{11}{50}\]

**Clearly state the answer showing the ‘decimal’ = ‘fraction’**

\[0.22=\frac{11}{50}\]

Convert

**Write the decimal as a fraction by dividing by 1**

\[0.385\div1\]

\[\frac{0.385}{1}\]

The lowest value in the number

This means if we multiply

If you only multiplied the numerator by

\[\frac{0.385}{1}\]

\[\frac{0.385\times1000}{1\times1000}\]

\[\frac{385}{1000}\]

**Simplify the fraction if possible**

\frac{385}{1000} can be simplified by dividing the numerator and denominator by

\[\frac{385\div5}{1000\div5}\]

\[\frac{77}{200}\]

**Clearly state the answer showing the ‘decimal’ = ‘fraction’**

\[0.385=\frac{77}{200}\]

Convert

**Write the decimal as a fraction by dividing by 1**

\[1.4\div1\]

\[\frac{1.4}{1}\]

The lowest value in the number

This means if we multiply

If you only multiplied the numerator by

\[\frac{1.4}{1}\]

\[\frac{1.4\times10}{1\times10}\]

\[\frac{14}{10}\]

**Simplify the fraction if possible**

\frac{14}{10} can be simplified by dividing the numerator and denominator by

\[\frac{14\div2}{10\div2}\]

\[\frac{7}{5}\]

**Clearly state the answer showing the ‘decimal’ = ‘fraction’**

\[1.4=\frac{7}{5}\]

*Note: This is an improper fraction, we could give this as a mixed number if required.*

E.g.

\[1.4=\frac{7}{5}=1\frac{2}{5}\]

Convert

**Write the decimal as a fraction by dividing by 1**

\[1.55\div1\]

\[\frac{1.55}{1}\]

The lowest value in the number

This means if we multiply

If you only multiplied the numerator by

\[\frac{1.55}{1}\]

\[\frac{1.55\times100}{1\times100}\]

\[\frac{155}{100}\]

**Simplify the fraction if possible**

\frac{155}{100} can be simplified by dividing the numerator and denominator by

\[\frac{155\div5}{100\div5}\]

\[\frac{31}{50}\]

**Clearly state the answer showing the ‘decimal’ = ‘fraction’**

\[1.55=\frac{31}{50}\]

Convert

**Write the decimal as a fraction by dividing by 1**

\[20.0006\div1\]

\[\frac{20.0006}{1}\]

The lowest value in the number

This means if we multiply

If you only multiplied the numerator by

\[\frac{20.0006}{1} \]

\[\frac{20.0006\times10000}{1\times10000}\]

\[\frac{20006}{10000}\]

**Simplify the fraction if possible **

\frac{20006}{10000} can be simplified by dividing the numerator and denominator by

\[\frac{200006\div2}{100000\div2}\]

\[\frac{100003}{5000}\]

**Clearly state the answer showing the ‘decimal’ = ‘fraction’**

\[20.0006=\frac{100003}{5000}\]

**Multiplying by an incorrect multiple of**10

You must multiply by a multiple of

E.g.

**Simplifying the fraction**

The question may say “give your answer in the simplest form”. Always take a moment to see if the fraction can be simplified.

**Not multiplying the denominator by the same as the numerator**

When you multiply the numerator by a multiple of

Decimals to fractions is part of our series of lessons to support revision on comparing fractions, decimals and percentages. You may find it helpful to start with the main comparing fractions, decimals and percentages lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

1. Which is the correct conversion of 0.1 to a fraction in its simplest form?

\frac{10}{100}

\frac{1}{10}

\frac{0.1}{1}

\frac{0.01}{100}

0.1 written as a fraction is \frac{10}{100} . We can simplify this by dividing both the numerator and denominator by 10 .

2. Which is the correct conversion of 0.4 to a fraction in its simplest form?

\frac{40}{100}

\frac{4}{10}

\frac{2}{5}

\frac{0.4}{1}

0.4 written as a fraction is \frac{40}{100} . We can simplify this by dividing both the numerator and denominator by 20 .

3. Which is the correct conversion of 1.1 to a fraction in its simplest form?

\frac{1.1}{1}

\frac{11}{10}

\frac{110}{100}

\frac{1}{10}

We can convert 1.1 to a fraction by writing it over 1 and multiplying the numerator and denominator by 10 .

4. Which is the correct conversion of 0.006 to a fraction in its simplest form?

\frac{0.006}{1}

\frac{6}{1}

\frac{6}{1000}

\frac{3}{500}

0.006 written as a fraction is \frac{6}{1000} . We can simplify this by dividing both the numerator and denominator by 2 .

5. Which is the correct conversion of 30.05 to a fraction in its simplest form?

\frac{601}{20}

\frac{1}{20}

30 \frac{1}{20}

\frac{3005}{1000}

We can convert 30.05 to a fraction by writing it over 1 and multiplying the numerator and denominator by 100 to give \frac{3005}{1000} . We can simplify this by dividing both the numerator and denominator by 5 .

6. Which of the below is not the fractional equivalent of 0.12 ?

\frac{84}{700}

\frac{12}{100}

\frac{6}{50}

\frac{12}{10}

\frac{12}{10} is equivalent to 1.2 not 0.12 .

1. Convert each of the following decimals to fractions. All answers must be given in their simplest form

a) 0.7

b) 0.75

c) 0.07

d) 0.007

e) 7.7

**(5 marks)**

Show answer

\frac{7}{10}

**(1)**

**(1)**

**(1)**

**(1)**

**(1)**

2. Convert each of the following decimals to fractions in their simplest form

a) 0.34

b) 1.12

c) 1.72

**(6 marks)**

Show answer

1 mark for any correct fraction given which is not in its simplest form

a) \frac{34}{100}

**(1)**

OR

\frac{17}{50}**(2)**

b) \frac{112}{100}

**(1)**

OR

\frac{28}{25}**(2)**

c) \frac{172}{100}

**(1)**

OR

\frac{43}{25}**(2)**

3. Match each decimal to the correct fraction below

\frac{3}{5}, \frac{1}{4} , \frac{7}{5}, \frac{26}{5}, \frac{1}{100} Q3

a) 0.25

b) 1.4

c) 0.6

d) 0.01

e) 5.2

**(5 marks)**

Show answer

0.25=\frac{1}{4}

**(1)**

1.4=\frac{7}{5}

**(1)**

0.6=\frac{3}{5}

**(1)**

0.01=\frac{1}{100}

**(1)**

5.2=\frac{26}{5}

**(1)**

4. Show 0.888 as a fraction in its simplest form

**(2 marks)**

Show answer

1 mark for any correct fraction given which is not in its simplest form

\frac{888}{1000}

**(1)**

**(1)**

You have now learned how to:

- Convert a decimal to a fraction
- Give a fraction in its simplest form

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