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# 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%

## Example Values

Here is a table of commonly occuring 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

## Converting Between Percentage and Decimal

Percentage means "per 100", so 50% means 50 per 100, or simply 50/100. If you divide 50 by 100 you get 0.5 (a decimal number). So:

The easiest way to multiply (or divide) by 100 is to move the decimal point 2 places. So:

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

... or ...

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

## Converting Between Fractions and Decimals

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

Answer: 2/5 = 0.4

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

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

Then 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 it a correctly formed fraction) = 75 / 100

Then Simplify the fraction 3 / 4

## Converting Between Percentages and Fractions

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
Add the "%" sign: 37.5%

Answer: 3/8 = 37.5%

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