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Fractions, decimals and percentages

Tutor: Daniel

# Fractions, decimals and percentages

## ​​In a nutshell

Fractions, decimals and percentages can all be used to represent numbers. Percentages are typically used for comparing one quantity against another, while fractions and decimals are used to represent quantities.

## Converting between fractions and decimals

### ​​Fractions to decimals

To convert from a fraction to a decimal, perform short division by dividing the numerator by the denominator to obtain the decimal form.

### Decimals to fractions

#### ​​Procedure

 1 For terminating decimals, multiply the decimal by a number like $10$ or $100$ to make the last digit of the decimal move to the units column. This forms the numerator. 2 The denominator of the fraction is the number you multiplied by in step 1 ($10$ or $100$​ etc). 3 Simplify the fraction (if required).

##### Example 1

Convert $1.375$​ into a fraction in its simplest form.

$1.375 \times 1000 = 1375$

Hence $1.375 = \dfrac{1375}{1000}=\dfrac{275}{200} =\dfrac{55}{40}= \underline{\dfrac{11}{8}}$

## Converting between decimals and percentages

### Decimals to percentages

To convert from a decimal to a percentage, multiply the decimal by $100$ and put a $\%$​ sign at the end of the number.

### Percentages to decimals

To convert from a percentage to a decimal, divide the percentage by $100$ and remove the $\%$​ sign at the end of the number.

## Converting between fractions and percentages

In order to convert between fractions and percentages use the decimal form as an intermediate step.

##### Example 2

The following are examples of the same number in fraction, decimal and percentage form:

$\dfrac{3}{5} = 0.6 = 60\%$

$\dfrac{17}{4} = 4.25 = 425\%$

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## FAQs - Frequently Asked Questions

### How do you change a decimal to a percentage?

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