# How do I convert 0.75 to a common fraction?

I know you get 75 over 100, and the answer is 3 over 4. How do I simplify the 75 over 100 to change it into 3 over 4?

Step 1: Write down the decimal divided by 1, like this: decimal/1 Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.) Step 3: Simplify (or reduce) the fraction

Example: Express 0.75 as a fraction Step 1: Write down 0.75 divided by 1: 0.75 1 Step 2: Multiply both top and bottom by 100 (there were 2 digits after the decimal point so that is 10×10=100): × 100

0.75 = 75 1 100

× 100 (Do you see how it turns the top number into a whole number?) Step 3: Simplify the fraction (this took me two steps): ÷5 ÷ 5

75 = 15 = 3 100 20 4

``````÷5     ÷ 5
``````

You know how to get the 75/100 so ..... . ..... If you know about prime factors, "factorize" the numerator (75) and the denominator (100) to express them in their prime factors, ..... . ..... then cancel all "common factors" that appear in both the numerator and the denominator.
The prime factors that don't cancel out then give what you are looking for: . i.e. ..... 75 / 100 = ( 3 x 5 x 5 ) / ( 2 x 2 x 5 x 5 ) . = 3 / ( 2 x 2 ) ..... [ after cancelling the two 5's that appear in numerator & denominator ] . = 3 / 4 ‾‾‾‾‾‾‾‾‾‾ [ after multiplying any prime factors still left on "top" and/or "bottom" ]

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Best wishes - Majikthise. .