Decimals, Fractions and Percentages

Decimals, Fractions and Percentages are just different ways of showing the same value:

pizza 1/2

A Half can be written...

... as a fraction: 1 2

... as a decimal: 0.5

... as a percentage: 50%


pizza 1/4

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:

numbers/images/ani-frac-num-pct.js

Example Values

Here is a table of commonly used 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
33 1/3 % 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.

An easy way to divide by 100 is to move the decimal point 2 places to the left:

From Percent To Decimal
percent to decimal move the decimal point 2 places to the left

Don't forget to remove the % sign!

From Decimal to Percent

To convert from decimal to percent multiply by 100%

An easy way to multiply by 100 is to move the decimal point 2 places to the right:

From Decimal To Percent
decimal to percent move the decimal point 2 places to the right

 Don't forget to add the % sign!

From Fraction to Decimal

To convert a fraction to a decimal divide the top number by the bottom number:

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

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 a correctly formed fraction:

75 100

Then Simplify the fraction:

3 4

From Fraction to Percentage

To convert a fraction to a percentage divide the top number by the bottom number, then multiply the result by 100%

Example: Convert 3 8 to a percentage

First divide 3 by 8: 3 ÷ 8 = 0.375

Then multiply by 100%: 0.375 × 100% = 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

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 a correctly formed fraction:

8 10

Then Simplify the fraction:

4 5

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