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Decimals, Fractions and Percentages
Decimals, Fractions and Percentages are just different ways of showing the same value:
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Here, have a play with it yourself:
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 | |
 |
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
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 = 37.5
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 | 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 |
