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
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
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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