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In order to access this I need to be confident with:

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: We can also convert recurring decimals to fraction**s.

In order to convert from a 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**

\[0.385\div1\]

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

**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

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

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

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

**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**

\[1.4\div1\]

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

**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

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

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

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

**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

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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