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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.

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

Percentage to decimal 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. 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

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