decimal to fraction

decimal to fraction

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Decimal to fraction

The process of decimal to fraction conversion involves the use of 
the fundamental rule of fractions; the fraction should be written 
in its lowest terms.  The following examples demonstrate how to 
convert decimals to fractions. 

Example 1: 

Convert 0.65 to a fraction. 

Solution: 

Step 1: 

Note the number of place positions to the right of the decimal 
point. In this example, 0.65 is 65 hundredths, which is two places 
to the right of the decimal point. 

    65 
   ----
   100 

Step 2: 

Although we have now converted the decimal into a fraction, the 
fraction is not in its lowest terms. To reduce the new fraction 
into its lowest or simplest terms, both the numerator and the 
denominator must be broken down into primes. 



    65     5x13    5x13        5x13
   ---- >  ---- > ------- > ---------
   100     5x20    5x4x5     5x2x2x5

Note that we can cancel one set of 5s, 

          5
because  --- = 1
          5 
  
This gives 

     65     13
    ---- = ----          
    100     20 

and this is the simplest form of this fraction.