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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.