Key points
- A fraction expressed as the number of parts per hundred and recorded using the notation % are always out of 100. This is important to remember when converting percentages to fractions and decimals.
- Being able to To reduce a fraction to its simplest form, also known as its lowest terms. fractions and work out A fraction with the same value as another. will make converting percentages to fractions easier.
- Knowing how to multiply by 100 is a useful skill when converting a percentage to a decimal.
How to convert a percentage to a fraction
- Write the percentage value as the Number written at the top of a fraction. The numerator is the number of parts used. Eg, for 1⁄3, the numerator is 1 of the fraction.
- The Number written on the bottom of a fraction. The denominator is the number of equal parts. Eg, for 1⁄3, the denominator is 3 of the fraction is 100
- To reduce a fraction to its simplest form, also known as its lowest terms.the fraction if possible by dividing the numerator and denominator by their The largest factor that will divide into the selected numbers. Eg, 10 is the highest common factor of 30 and 20. Highest common factor is written as HCF. (HCF). The HCF is found by finding all A whole number which is a factor of two or more numbers. Eg, 2, 5 and 10 are common factors of 30 and 20 of two numbers and selecting the largest one.
If the numerator is a decimal, multiply the numerator and denominator by the lowest The second power of 10 for example is 100. Powers of 10 are 10, 100, 1000 and so on. to get a whole number value. Then simplify the fraction.
Examples
Image caption, Convert 36% to a fraction.
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Question
What is 60% as a fraction?
The fraction for 60% has a numerator of 60 and a denominator of 100
This can be simplified by dividing the numerator (60) and the denominator (100) by their HCF (20)
60% is \( \frac{3}{5} \)
How to convert a percentage to a decimal
To convert a percentage to a decimal, divide the percentage value by 100
Examples
Image caption, Convert 36% to a decimal.
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Question
What is 60% as a decimal?
To convert a percentage to a decimal, divide the percentage value by 100
60 ÷ 100 = 0∙6
60% is 0∙6
Practise converting percentages to fractions and decimals
Try this quiz to practise converting percentages to fractions and decimals.
Quiz
Real-world maths
A business may choose to convert a percentage to a fraction or decimal when thinking about advertising and marketing.
A subscription service running a discount may choose to convert a percentage to a fraction when advertising this discount. For example, ‘half price’ may attract more potential customers than ‘50% off’.
Game - Divided Islands
Play the Divided Islands game! game
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