Decimals, Fractions and Percentages

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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:

Example Values

Here is a table of commonly occuring values shown in Percent, Decimal and Fraction form:

PercentDecimalFraction
1%0.011/100
5%0.051/20
10%0.11/10
12½%0.1251/8
20%0.21/5
25%0.251/4
331/3%0.333…1/3
50%0.51/2
75%0.753/4
80%0.84/5
90%0.99/10
99%0.9999/100
100%1
125%1.255/4
150%1.53/2
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 PercentTo 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 DecimalTo 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

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
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

StepsExample
Convert 80% to a decimal (=80/100):0.8
Write down the decimal “over” the number 10.8 / 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 fraction4 / 5

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