Key points
In the decimal system 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 units. are all The second power of 10 for example is 100. Powers of 10 are 10, 100, 1000 and so on. . This helps when converting decimals to fractions.
Understanding To reduce a fraction to its simplest form, also known as its lowest terms. can be useful when converting decimals and fractions. When a decimal converted to a fraction is not in its lowest terms it should be simplified.
To convert fractions to decimals, understanding place value, equivalent fractions as well as division can be useful.
How to convert a decimal to a fraction
To convert a decimal to a fraction:
It can be useful to think about place value. The final digit’s place value gives 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.
Starting from the first non-zero digit, the digits of the decimal number gives 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.
The fraction may be simplified when the numerator and denominator have a common factor greater than one.
Units are often referred to as ones. Eg, 4∙2 has 4 units and 2 tenths, or you could say 4∙2 has 4 ones and 2 tenths.
Examples
Image caption, Use place value to convert decimals to fractions.
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Question
Convert 0∙85 to a fraction.
The final digit has a hundredth place value. The denominator is 100
The numerator is 85
0∙85 is \( \frac{85}{100} \)
This can be simplified to \( \frac{17}{20} \)
How to convert a fraction to a decimal using equivalent fractions
To convert a fraction to a decimal when the denominator is a factor or multiples of powers of ten:
Write an equivalent fraction with a denominator that is a power of ten.
Use place value to convert this fraction to a decimal.
Examples
Image caption, A fraction is one way of writing a division. The numerator is divided by the denominator. Fractions can be converted into decimals by processing this division. Convert 3⁄5 to a decimal.
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Question
Convert \( \frac{21}{25} \) to a decimal.
\( \frac{21}{25} \) is equivalent to \( \frac{84}{100} \)
\( \frac{84}{100} \) is 0∙84
\( \frac{21}{25} \) is 0∙84 as a decimal.
How to convert a fraction to a decimal using division
Fractions can be converted into decimals by division. This method works for converting any fraction to a decimal:
Divide the numerator by the denominator.
Understanding short division can be helpful when using this method.
Examples
Image caption, A fraction is one way of writing a division. The numerator is divided by the denominator. Fractions can be converted into decimals by processing this division. Convert 3⁄5 to a decimal. 3⁄5 means 3 ÷ 5
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Question
Convert \( \frac{7}{8} \) to a decimal.
\( \frac{7}{8} \) means 7 ÷ 8
7 ÷ 8 is 0∙875
\( \frac{7}{8} \) is 0∙875 as a decimal.
Practise converting fractions to decimals
Quiz
Practise converting fractions to decimals. You may want to use a pen and paper to help you with your workings out.
Real-world maths
Converting fractions into decimals can help when converting currencies.
To convert between currencies an exchange rate is used. An exchange rate compares two currencies.
For example if £10 is the same as €9 then the fraction \( \frac{9}{10} \) is converted to the decimal 0∙9. This decimal can then be used to change pounds sterling into euros (£ × 0∙9 = €) or euros to pounds (€ ÷ 0∙9 = £).
Game - Divided Islands
Divided Islands. game
Use your maths skills to help the islanders of Ichi build bridges and bring light back to the islands in this free game from BBC Bitesize.
More on Fractions
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