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Place value Arithmetic To the power of Mixed number to improper fractionThis topic is relevant for:
Here we will learn about converting fractions to decimals.
There are also converting fractions to decimals worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.
Converting fractions to decimals is representing a fraction as a decimal without changing its value.
E.g.
\begin{aligned} &\frac{1}{4}=0.25\\\\ &\frac{1}{8}=0.125\\\\ &\frac{2}{7}=0.2857142857β¦\\\\ &3 \frac{1}{5}=3.2 \end{aligned}In order to convert from a fraction to a decimal you need to:
Get your free fractions to decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.
COMING SOONGet your free fractions to decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.
COMING SOONConvert \frac{1}{2} to a decimal.
There is no need to convert as the fraction is already in the correct form.
2Divide the numerator by the denominator.
1 \div 2 \quad \quad \quadUsing the βbus stop methodβ:
3State the answer clearly in the form βfractionβ=βdecimalβ.
\frac{1}{2} = 0.5Convert \frac{3}{8} to a decimal
If needed convert the mixed number to an improper fraction.
There is no need to convert as the fraction is already in the correct form.
Divide the numerator by the denominator.
State the answer clearly in the form βfractionβ=βdecimalβ.
Convert \frac{7}{5} to a decimal
If needed convert the mixed number to an improper fraction.
There is no need to convert as the fraction is already in the correct form.
Divide the numerator by the denominator.
State the answer clearly in the form βfractionβ=βdecimalβ.
Convert 3 \frac{1}{4} to a decimal
If needed convert the mixed number to an improper fraction.
You need to convert this mixed number to an improper fraction.
3 \frac{1}{4}= \frac{13}{4}
Step by step guide: Improper fractions and mixed numbers (coming soon)
Divide the numerator by the denominator.
State the answer clearly in the form βfractionβ=βdecimalβ.
Convert \frac{2}{9} to a decimal.
If needed convert the mixed number to an improper fraction.
There is no need to convert as the fraction is already in the correct form.
Divide the numerator by the denominator.
You will notice here that the 2 is repeated and will continue to be repeated. This is therefore a recurring decimal and can be shown in the form 0.\dot{2} .
State the answer clearly in the form βfractionβ=βdecimalβ.
Convert 2\frac{1}{7} to a decimal.
If needed convert the mixed number to an improper fraction.
You need to convert this mixed number to an improper fraction.
2\frac{1}{7}=\frac{15}{7}
Step by step guide: Improper fractions and mixed numbers (coming soon).
Divide the numerator by the denominator.
You will notice here that the 1 4 2 8 5 7 after the decimal place is repeated and will continue to be repeated. This is therefore a recurring decimal and can be shown as 2.\dot{1}4285\dot{7} .
State the answer clearly in the form βfractionβ=βdecimalβ.
You can check your answer on a calculator by inputting the fraction into your calculator and then pressing the [S β D] button.
E.g.
Convert \frac{5}{4} to a decimal.
1. Press the fraction button on the left hand side of your calculator.
2. Input the numbers and press the = button.
3. Press the [S β D] button to have it shown as a decimal.
Therefore \frac{5}{4}=1.25 .
A common error is to incorrectly convert between numbers in different forms
E.g.
Mixed numbers and improper fractions.
A common error is to incorrectly use a written method of division
E.g. the bus stop method or other methods of long division.
A common error is to divide the denominator by the numerator rather than dividing the numerator by the denominator.
E.g.
\frac{5}{7} means 5 \div 7 not 7 \div 5
Fractions to decimals 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 \frac{1}{4} to a decimal
1 Γ· 4 gives the decimal 0.25
2. Convert \frac{7}{8} to a decimal
7 Γ· 8Β gives the correct decimal 0.875
3. Convert \frac{7}{4} to a decimal
7 Γ· 4Β gives the correct decimal 1.75
4. Convert 7\frac{3}{5} to a decimal
Converting to an improper fraction gives \frac{38}{5} , then you divide the numerator by the denominator.
5. Convert \frac{4}{9} to a decimal
Calculating 4\div9 gives the recurring decimal 0.\dot{4} . The dot above the 4 means that the 4 is repeated infinitely.
6. Convert \frac{2}{11} to a decimal
Calculating 2\div11 gives the recurring decimal 0.\dot{1}\dot{8} . The dot above the 1 and 8 represents the 1 and 8 being repeated infinitely
1.Β a) Convert \frac{1}{2} to a decimal
b) Convert \frac{1}{4} to a decimal
c) Convert \frac{3}{5} to a decimal
(3 marks)
a) 0.5
(1)
b) 0.25
(1)
c) 0.6
(1)
2.Β a) Convert 2\frac{1}{2} to a decimal
b) Convert \frac{8}{5} to a decimal
c) Convert \frac{1}{3} to a decimal
(3 marks)
a) 2.5
(1)
b) 1.6
(1)
c) 0. \dot{3}
Must be shown to be recurring
Accept 0.333333β¦
(1)
3.Β a) Convert \frac{7}{10} to a decimal
b) Convert \frac{2}{25} to a decimal
c) Convert \frac{2}{9} to a decimal
(3 marks)
a) 0.7
(1)
b) 0.08
(1)
c) 0. \dot{2}
Must be shown to be recurring
Accept 0.222…
(1)
You have now learned how to:
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