# Decimals, Fractions and Percentages

Decimals, Fractions and Percentages are just different ways of showing the same value:

 A Half can be written... As a fraction: 1/2 As a decimal: 0.5 As a percentage: 50%

 A Quarter can be written... As a fraction: 1/4 As a decimal: 0.25 As a percentage: 25%

Here, have a play with it yourself:

## Example Values

Here is a table of commonly used values shown in Percent, Decimal and Fraction form:

Percent Decimal Fraction
1% 0.01 1/100
5% 0.05 1/20
10% 0.1 1/10
12½% 0.125 1/8
20% 0.2 1/5
25% 0.25 1/4
331/3% 0.333... 1/3
50% 0.5 1/2
75% 0.75 3/4
80% 0.8 4/5
90% 0.9 9/10
99% 0.99 99/100
100% 1
125% 1.25 5/4
150% 1.5 3/2
200% 2

## Conversions

#### From Percent to Decimal

To convert from percent to decimal: divide by 100, and remove the "%" sign.

The easiest way to divide by 100 is to move the decimal point 2 places to the left:

 From Percent To Decimal move the decimal point 2 places to the left, and remove the "%" sign.

#### From Decimal to Percent

To convert from decimal to percent: multiply by 100, and add a "%" sign.

The easiest way to multiply by 100 is to move the decimal point 2 places to the right:

 From Decimal To Percent move the decimal point 2 places to the right, and add the "%" sign.

#### From Fraction to Decimal

The easiest way to convert a fraction to a decimal is to divide the top number by the bottom number (divide the numerator by the denominator in mathematical language)

### Example: Convert 2/5 to a decimal

Divide 2 by 5: 2 ÷ 5 = 0.4

#### From Decimal to Fraction

To convert a decimal to a fraction needs a little more work.

### Example: To convert 0.75 to a fraction

Steps Example
First, write down the decimal "over" the number 1
 0.75 1

Multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc)
 0.75 × 100 1 × 100
(This makes a correctly formed fraction)
 75 100
Then Simplify the fraction
 3 4

#### From Fraction to Percentage

The easiest way to convert a fraction to a percentage is to divide the top number by the bottom number. then multiply the result by 100, and add the "%" sign.

### Example: Convert 3/8 to a percentage

First divide 3 by 8: 3 ÷ 8 = 0.375,
Then multiply by 100: 0.375 x 100 = 37.5

#### From Percentage to Fraction

To convert a percentage to a fraction, first convert to a decimal (divide by 100), then use the steps for converting decimal to fractions (like above).

### Example: To convert 80% to a fraction

Steps Example
Convert 80% to a decimal (=80/100): 0.8

Write down the decimal "over" the number 1
 0.8 1

Multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc)
 0.8 × 10 1 × 10
(This makes a correctly formed fraction)
 8 10
Then Simplify the fraction
 4 5