Decimals, Fractions and Percentages

Decimals, Fractions and Percentages are just different ways of showing the same value:
external image pie-1-2.jpg
A Half can be written...


As a fraction:
1/2
As a decimal:
0.5
As a percentage:
50%

external image pie-1-4.jpg
A Quarter can be written...


As a fraction:
1/4
As a decimal:
0.25
As a percentage:
25%
Try this interactive activity

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

external image percent-to-decimal.gif
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

external image decimal-to-percent.gif
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 = 37.5Add 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


Now look at understanding percentage questions.

Source:

http://www.mathsisfun.com/decimal-fraction-percentage.html