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:

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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

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. So:

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. So:

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
Answer: 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
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

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
Add the "%" sign: 37.5%
Answer: ³/₈ = 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
Then 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 it a correctly formed fraction)	= 8 / 10
Then Simplify the fraction	4 / 5

Posted in: Decimal Number, Decimals-Fractions- Percentages, Fractions, Number System