How do you convert a fraction into a decimal

How to convert between fractions and decimals

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Key points

• In the decimal system are all . This helps when converting decimals to fractions.

• Understanding 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 .

• Starting from the first non-zero digit, the digits of the decimal number gives the .

• 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

Use place value to convert decimals to fractions.

Convert the decimal 0∙8 to a fraction.

The final digit has a place value of tenths. The denominator is tenths. The numerator is 8. 0∙8 is 8⁄10 as a fraction. This can be simplified to 4⁄5

Convert the decimal 4∙23 to a fraction.

The final digit has a hundredths place value. The denominator is 100. The numerator is 423. 4∙23 is 423⁄100 as a fraction. This is also 4 23⁄100. 4 23⁄100 is a mixed number and cannot be simplified.

Convert the decimal 0∙015 to a fraction.

The final digit has a thousandth place value. The denominator is 1000. The numerator is 15. 0∙015 is 15⁄1000 as a fraction.

0∙015 is 15⁄1000 and can be simplified to 3⁄200

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:

1. Write an equivalent fraction with a denominator that is a power of ten.

2. Use place value to convert this fraction to a decimal.

Examples

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.

5 is a factor of 10. 5 x 2 = 10. Find the equivalent fraction for 3⁄5 by multiplying the numerator and denominator by 2. 3⁄5 is equivalent to 6⁄10

3⁄5 is equivalent to 6⁄10. 6⁄10 is 0∙6. 3⁄5 is 0∙6 as a decimal.

Convert 13⁄20 to a decimal.

20 is a multiple of 10. 20 ÷ 2 is 10. 20 is also a factor of 100. 20 x 5 is 100. Find the equivalent fraction that is easiest to work out.

13 ÷ 2 is not a whole number. 13 multiplied by 5 is easier. 13 x 5 = 65. 13⁄20 is equivalent to 65⁄100

13⁄20 is equivalent to 65⁄100. 65⁄100 is 0∙65. 13⁄20 is 0∙65 as a decimal.

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

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

3 divided by 5 is 0∙6 . 3⁄5 is 0∙6 as a decimal.

Convert 1⁄8 to a decimal. 1⁄8 means 1 ÷ 8

1 ÷ 8 is 0∙125. 1⁄8 is 0∙125 as a decimal.

Convert 4⁄9 to a decimal. 4⁄9 means 4 ÷ 9

4⁄9 is 0∙444444444… This is a recurring decimal. This is shown with a dot above the recurring digit.

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 = £).

Converting fractions into decimals can help when converting currencies.