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# 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.
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