.33 As A Fraction

How is 0.33 converted to 1/3? Multiplying by 100 gives 33/100 which can't be reduced. So what am I doing wrong?


Asked on by jp---46

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The fractions obtained by dividing 1 by 3 is equal to 0.3333... the series of 3 after the decimal point goes on for ever.

To convert 0.33 to a fraction you would have to use approximation, approximating the recurring decimal obtained when 1 is divided by 3 gives 0.33.

This is what makes 0.33 approximately equal to 1/3 though the exact result is 33/100.


Here is some more information on how to turn a repeating decimal (a decimal that goes on forever) into a fraction.

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

If you divide 1 by 3 by hand in the long way you get this: 

Its a never ending and repeating decimal : 0.3333333333333333333333333...

But its not practical to just keep on writing this, is it? So we just use a short cut of .33 . Its basically understood by mathematicians as to what you're referring to. 

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