One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

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

Percentage to decimalPlace value

Simplifying fractions

Equivalent fractions Improper fractions and mixed numbersAdding and subtracting

FractionsThis topic is relevant for:

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

There are also decimals to percentages 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 **decimal to percentage** is representing the decimal as a percentage without changing its value.

E.g.

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

In order to convert decimal numbers to percentages you need to:

**Multiply the decimal by \pmb{100} and add the percent sign (%) (because percent means out of \pmb{100}).***Note: If working with a recurring decimal you need to ensure you still have the recurring aspect of the decimal*.**Clearly state the answer showing the ‘decimal value’ = ‘percentage value’.**

To learn how to convert percentages to decimals check out:

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

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

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

COMING SOONConvert

**Multiply the decimal by a hundred and add the percentage sign (**% ).

\[0.7\times100=70\%\]

The

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

\[0.7=70\%\]

Convert

** Multiply the decimal by a hundred and add the percentage sign (%) **

\[\begin{aligned}
&0.625\times100\\\\
&62.5\%
\end{aligned}\]

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

\[0.625 =62.5\%\]

Convert

**Multiply the decimal by a hundred and add the percentage sign (%)**

\[1.23\times100=123\%\]

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

\[1.23=123\%\]

Convert

** Multiply the decimal by a hundred and add the percentage sign (%) **

\[0.006\times100=0.6\%\]

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

\[0.006=0.6\%\]

Convert 0.\dot{2} to a percentage.

** Multiply the decimal by a hundred and add the percentage sign (%) **

\[0.\dot{2} \times 100\]

For this step you need to remember that the 2 is recurring; this means it is repeated infinitely.

0.\dot{2}=0.222222222222…

So when you multiply the recurring decimal by 100 you still have the recurring 2.

Therefore

\[0.\dot{2}\times100= 22.\dot{2}\]

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

\[0.\dot{2}= 22.\dot{2}\%\]

Convert 0.\dot{1}4285\dot{7} to a percentage.

** Multiply the decimal by a hundred and add the percentage sign (%) **

\[0.\dot{1}4285\dot{7} \times 100\]

For this step you need to remember that the 142857 is recurring; this means it is repeated infinitely.

\[ 0.\dot{1}4285\dot{7}=0.142857142857142857142857…\]

So,

\[ 0.\dot{1}4285\dot{7} \times 100 =14.2857142857142857142857…\]

Therefore

\[\begin{aligned}
& 0.\dot{1}4285\dot{7} \times 100 =14.\dot{2}8571\dot{4} \\\\
&14.\dot{2}8571\dot{4} \%
\end{aligned}
\]

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

\[0.\dot{1}4285\dot{7} =14.\dot{2}8571\dot{4} \% \]

If you are allowed to use a calculator for the questions, you can perform the operation in one calculation.

E.g.

Convert 1.057 to a percentage.

**Enter the decimal on the calculator and multiply by \pmb{100}.****Press = (this will normally give you the answer in fraction form).****Press the \pmb{S ⇔ D} button to convert a decimal.****This means \pmb{ 1.057= 105.7\% }.**

**Mistakes with multiplication of \pmb{100}**

Often mistakes are made when multiplying a value by 100 by moving the digits the incorrect number of decimal places.

**Not adding a percentage sign**

Percentages must end in a percentage sign

E.g.

50 is not a percentage but 50\% is.

**Not noticing a recurring decimal**

Sometimes a recurring decimal is not immediately obvious.

E.g.

\frac{1}{7}=0.142857142857142857..

Therefore,

\frac{1}{7}= 0.\dot{1}4285\dot{7}

Decimal to percentage 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 0.01 to a percentage

1\%

10\%

0.1\%

0.01\%

0.01 has been correctly multiplied by 100.

2. Convert 0.4 to a percentage

40\%

4\%

0.4\%

40

0.4 has been correctly multiplied by 100.

3. Convert 1.1 to a percentage

11\%

1.1\%

110

110\%

1.1 has been correctly multiplied by 100.

4. Convert 0.006 to a percentage

0.6

0.06\%

6\%

0.6\%

0.006 has been correctly multiplied by 100.

5. Convert 30.05 to a percentage

30.05\%

3005\%

3005

305\%

30.05 has been correctly multiplied by 100.

6. Convert 0.\dot{4} to a percentage

44.\dot{4}\%

44\%

44.4\%

0.\dot{4}\%

44.\dot{4}\% has been correctly multiplied by 100.

1. Convert each of the following decimals to percentages:

a) 0.09

b) 0.25

c) 0.9

d) 0.007

e) 6.6

**(5 marks)**

Show answer

a) 9\%

**(1)**

b) 25\%

**(1)**

c) 90\%

**(1)**

d) 0.7\%

**(1)**

e) 660\%

**(1)**

2. Convert each of the following decimals to percentages:

a) 0.31

b) 0.887

c) 0.7\dot{3}

**(4 marks)**

Show answer

a) 31\%

**(1)**

b) 88.7\%

**(1)**

c) 73.33333…\% or 73.\dot{3}

**(1)**

3. Match the decimals to the percentage.

\begin{aligned}
&0.41 \quad \quad \quad \;\;50\% \\
&0.5 \quad \quad \quad \;\;\;\;170\% \\
&1.7 \quad \quad \quad \;\;\;\;41\% \\
&2.6 \quad \quad \quad \;\;\;\;0.3\% \\
&0.003 \quad \quad \quad 260\% \end{aligned}

**(5 marks)**

Show answer

0.41=41\%

**(1)**

0.5=50\%

**(1)**

1.7=170\%

**(1)**

2.6=260\%

**(1)**

0.003=0.3\%

**(1)**

4. Represent 0.\dot{5} as a percentage.

You must show your working out at each stage.

**(2 marks)**

Show answer

0.\dot{5}\times100 or 55.\dot{5} seen

**(1)**

55.\dot{5}\%

**(1)**

You have now learned how to:

- Convert a decimal to a percentage
- Convert a recurring decimal to a percentage

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths revision programme.