Notes for Decimals, Fractions and Percentages
September 5th, 2014Decimals, 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 is a table of commonly occurring 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} 
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
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  

First, write down the decimal “over” the number 1


Multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc)


(This makes a correctly formed fraction)


Then Simplify the fraction

**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


Multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc)


(This makes a correctly formed fraction)


Then Simplify the fraction
