Key points about conversion of fractions, decimals and percentages
Converting between fractions, decimals and percentages is a useful problem-solving skill.
The data can be more easily ordered by size when written in the same format.
Calculations often give a decimal answer. Converting a decimal to a percentage makes the data easier to understand.
Refresh your knowledge with these guides on equivalent fractions and simplifying fractions.
Check your understanding
How to convert decimals to fractions and percentages
Converting a decimal to a fraction
The final digit’s The value of a digit that relates to its position or place in a number, eg in 1482 the digits represent 1 thousand, 4 hundreds, 8 tens and 2 ones. gives the Number written on the bottom of a fraction. The denominator is the number of equal parts, eg for ⅓, the denominator is 3..
Starting from the first non-zero digit, the digits of the decimal number give the Number written at the top of a fraction. The numerator is the number of parts used, eg for ⅓, the numerator is 1..
The fraction may be simplified when the numerator and denominator have a A whole number which is a factor of two or more numbers. 2, 5 and 10 are common factors of 30 and 20. greater than one.
Converting a decimal to a percentage
Multiply the decimal by 100 to get the percentage value.
Write the percentage value with the percentage symbol (%).
Decimals greater than 1 are greater than 100%.
Follow the working out below
GCSE exam-style questions
- Write the decimal 0·12 as a fraction.
\(\frac{3}{25} \)
The final digit has a hundredths place value, so the denominator is one hundred.
The numerator is 12.
\(\frac{12}{100}\) as a fraction can be simplified to \(\frac{3}{25} \).
- Write the decimal 4·5 as a percentage.
4·5 = 450%
Multiply the decimal by 100 to get the percentage value.
4·5 × 100 = 450
Game - Equivalent fractions and decimals
Practise your equivalent fractions and decimals skills with these puzzles from Divided Islands.
Play the full Divided Islands game.
How to convert fractions to decimals and percentages
Converting fractions to decimals
Fractions can be converted to a decimal by division.
- To write a fraction as a decimal, divide the numerator by the denominator.
Find out more about short division using the bus stop method.
Converting fractions to percentages
To convert a fraction to a percentage:
Convert the fraction to a decimal.
Convert the decimal to a percentage.
Follow the working out below
GCSE exam-style questions
- Write the fraction \(\frac{7}{8}\) as a decimal.
\(\frac{7}{8}\) = 0·875
Divide the numerator (7) by the denominator (8).
7 ÷ 8 = 0·875
- Write the fraction \(\frac{7}{30}\) as a decimal.
\(\frac{7}{30}\) = 0∙2333…
The decimal can be written \(0.2\dot{3}\).
Divide the numerator (7) by the denominator (30).
7÷30 = 0·2333…
Game - Equivalent fractions and percentages
Have a go at completing these puzzles from our Divided Islands maths game to practise converting fractions to decimals and percentages.
How to convert percentages to decimals and fractions
Converting a percentage to a decimal
Percent means per hundred (divide by 100).
- To convert a percentage to a decimal divide the percentage value by 100.
Converting a percentage to a fraction
Write the percentage value as the numerator of the fraction.
The denominator of the fraction is 100.
Simplify the fraction if possible:
For whole number values, divide the numerator and denominator by their The greatest factor that will divide into the selected numbers. 10 is the highest common factor of 30 and 20..
For a decimal numerator, first multiply the numerator and denominator by the least The power of ten tells us how many times to use the number in a multiplication. For example 10² means 10 × 10 = 100. Powers of ten are 10, 100, 1000 and so on. to get whole number values and then simplify the fraction.
Follow the working out below
GCSE exam-style questions
- Write the percentage 125% as a decimal.
The resulting decimal is 1·25.
Divide the percentage value (125) by 100.
125% = 1·25
- Write the percentage 65% as a fraction.
65% = \(\frac{13}{20}\)
Write the percentage value (65) as the numerator of the fraction.
The denominator of the fraction is 100.
The fraction can be simplified to \(\frac{13}{20}\).
Game - Equivalent percentages and decimals
Try these questions from our Divided Islands game and practise your equivalent percentages and decimals skills.
Quiz - Fractions, decimals and percentages
Practise what you've learned about converting between fractions, decimals and percentages with this quiz. The quiz will change the questions each time you try it so be sure to come back and test your knowledge.
Now you have revised converting between fractions, decimals and percentages, why not try this guide on multiples and factors?
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