Easy shortcut for converting a repeating decimal to a fraction

Wednesday, March 9, 2016

Easy shortcut for converting a repeating fraction to a decimal.

Converting a repeating decimal to a fraction can be a little tricky. 
I have created two videos that show two different methods for converting the repeating fraction to a fraction. 

It will be helpful if you also watch the videos as I work on several examples.

The first method involves generating a numerator and a denominator.

First, we will generate the numerator. 
If you only have repeating numbers like .222 you write the repeating number as your numerator.
If you have a mixed recurring decimal like .16666, subtract the 
the non-repeating number from the non-repeating number combined with the repeating number. 
Notice the 1 does not repeat like the 6.

In this example, the non-repeating number and the repeating number equals 16 minus the non-repeating number which is 1.
16-1 =15

The denominator rules are as follows, for non-repeating numbers a 0, and add a 9 for repeating numbers.
In this example .16666 add a 0 for the non-repeating 1 and a 9 for the repeating 6 which equals 90.
Therefore you get the fraction 15/90

Once you write the fraction you then reduce.
15/90 = 1/6

The video works the following example problems.

Convert .333 to a fraction

Convert .666 to a fraction

Convert .1818   

Convert .4166 

Convert .2518 

Convert .70643889889.

This shortcut works on all repeating fractions.

An alternate method for converting the repeating decimal to a fraction is to set the repeating fraction equal to x

After creating the original video and reading the comments I researched an alternate method. Now you have two ways to convert the repeating decimal to a fraction and you can decide which method you like best.


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