# Percents, Fractions, Decimals

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 occurring values shown in Percent, Decimal and Fraction form:

PERCENTDECIMALFRACTION
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%1 100/100
125%1.25 5/4
150%1.5 3/2
200% 2 4/2

## 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

### From Decimal to Fraction

To convert a decimal to a fraction needs a little more work.

### Example: To convert 0.75 to a fraction

STEPSEXAMPLE
First, write down the decimal “over” the number 10.75 / 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 fraction3 / 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

### 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

STEPSEXAMPLE
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 