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

Decimal to percentagePlace value

Multiplying and dividing by 10, 100, 1000

Simplifying fractions

Equivalent fractions Improper fractions and mixed numbersAdding and subtracting

FractionsThis topic is relevant for:

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

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

Converting a **percentage to decimal **is representing the percentage as a decimal without changing its value.

E.g.

\[\begin{aligned}
&25\%=0.25\\\\
&45 \%=0.45\\\\
&33.\dot{3} \%=0.33333 \ldots\\\\
&80 \%=0.8
\end{aligned}
\]

In order to convert from a percentage to a number in its decimal form you need to:

**Divide the percentage by \pmb{100} because the percent sign**(%) means out of one hundred.**Clearly state the answer showing the ‘percentage’ = ‘decimal’.**

To learn how to convert decimals to percentages check out:

**Step by step guide**: Decimal to Percentage

Get your free percentage to decimal worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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

COMING SOONConvert 60% to a decimal.

**Divide the percentage by a hundred since the percent sign (%) means out of \pmb{100}.**

You know that the percentage sign (%) means the number is out of 100. Therefore if we divide the number by a hundred we will have the equivalent decimal.

\[60\% = 60\div100=0.6\]

When we divide by 100 we move the digits two places to the right.

The 6 has moved from the tenths column to the tenths column in the first decimal place.

The 0 has moved from the units column (ones column) to the hundredths column in the second decimal place.

The decimal point does not move.

**2Clearly state the answer showing the ‘percentage’ = ‘decimal’**.

\[60\% = 0.6\]

Convert 8% to a decimal.

**Divide the percentage by a hundred.**

\[8\% = 8\div100=0.08\]

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

\[8\% = 0.08\]

Convert 52.3% to a decimal.

**Divide the percentage by a hundred.**

\[52.3\% = 52.3\div100=0.523\]

**Clearly state the answer showing the ‘percentage’ = ‘decimal’.**

\[52.3\% = 0.523\]

Convert 4.\dot{2} to a decimal.

**Divide the percentage by a hundred.**

\[4.\dot{2}\% = 4.\dot{2}\div100\]

** Note: **Remember the 2 is a recurring decimal. It will still be recurring indefinitely after being divided by 100.

E.g.

\[ 0.\dot{2}\div100= 0.00\dot{2}\]

Therefore,

\[4.\dot{2}\% = 4.\dot{2}\div100= 0.04\dot{2}\]

**Clearly state the answer showing the ‘percentage’ = ‘decimal’.**

\[4.\dot{2}\% = 0.04\dot{2}\]

Convert 145.1% to a decimal.

**Divide the percentage by a hundred.**

\[145.1\% = 145.1\div100=1.451\]

**Clearly state the answer showing the ‘percentage’ = ‘decimal’.**

\[145.1\% = 1.451\]

Convert 102.04% to a decimal.

**Divide the percentage by [a hundred.**

\[102.04\% = 102.04\div100=1.0204\]

**Clearly state the answer showing the ‘percentage’ = ‘decimal’.**

\[102.04\% = 1.0204
\]

Convert

**Insert the value of the percentage into your calculator.****Divide by \pmb{100}.****Press the**= button. Here your calculator will give the answer as a fraction in its simplest form.**Press the \pmb{[s ⇔ d]} button to have it shown as a decimal.**

12% = 0.12

**Multiplying incorrectly by \pmb{100}**

Often mistakes are made when dividing by 100. The common mistakes are:

− Dividing by 10 not 100.

− Multiplying instead of dividing.

− Making mistakes with decimals.

Make sure you are confident with the below calculations:

E.g.

\[\begin{aligned}
&4 \div 100=0.04 \\\\
&0.4 \div 100=0.004 \\\\
&0.04 \div 100=0.0004
\end{aligned}\]

**Recurring decimals in the percentages**

You need to remember to take the recurring decimal into account when multiplying by an order of 10.

E.g.

\[0.\dot{4}\times10=4.\dot{4} \; \text{not} \; 4.4
\]

1. Convert 25\% to a decimal

25

0.25

4

2.5

25\% means 25 ÷ 100 which is equal to 0.25

2. Convert 87.5\% to a decimal

1.\dot{1}4285\dot{7}

87.5

0.875

8.75

87.5\% means 87.5 ÷ 100 which is equal to 0.875

3. Convert 175\% to a decimal

1.75

0.175

175

17.5

175\% means 175 ÷ 100 which is equal to 1.75

4. Convert 760\% to a decimal

760

0.76

7.35

7.6

760\% means 760 ÷ 100 which is equal to 7.6

5. Convert 4. \dot{4}\% to a decimal

0.4

0.44

0.444

0.\dot{4}

44.\dot{4}\% means 44.\dot{4} ÷ 100 which is equal to 0.\dot{4}

6. Convert 18.\dot{1}\dot{8}\% to a decimal

0.18

0.181818

0. \dot{1}\dot{8}

1. \dot{8}\dot{1}

18.\dot{1}\dot{8}\% means 18.\dot{1}\dot{8} ÷ 100 which is equal to 0. \dot{1}\dot{8}

1.

a) Convert 52\% to a decimal.

b) Convert 25\% to a decimal.

c) Convert 80\% to a decimal.

**(3 marks)**

Show answer

a) 0.52

**(1)**

b) 0.25

**(1)**

c) 0.8

**(1)**

2.

a) Convert 250\% to a decimal.

b) Convert 160\% to a decimal.

c) Convert 20\% to a decimal.

**(3 marks)**

Show answer

a) 2.5

**(1)**

b) 1.6

**(1)**

c) 0.2

**(1)**

3.

a) Convert 70\% to a decimal.

b) Convert 8\% to a decimal.

c) Convert 22. \dot{2} to a decimal.

**(3 marks)**

Show answer

a) 0.7

**(1)**

b) 0.08

**(1)**

c) 0.\dot{2}

**(1)**

4.

a) Convert 101\% to a decimal.

b) Convert 16.\dot{6} to a decimal.

**(2 marks)**

Show answer

a) 1.01

**(1)**

b) 0.1\dot{6}

**(1)**

You have now learned how to:

- Convert percentages to a decimal
- Convert percentages (with a decimal) to a decimal
- Convert percentages (with a recurring decimal) to a decimal

- Comparing fractions, decimals and percentages
- Convert fractions to decimals.

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