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Repeating Decimal to a Fraction
Follow these rules for changing a recurring decimal to a fraction.
Changing a repeating decimal back to a fraction
Only repeating – write as your numerator
Mixed repeating and non-repeating – write the non-repeating number followed by the difference between the repeating and the non-repeating.
Non-repeating numbers add a zero
Repeating numbers add a 9
Once you write the fraction, you must reduce it.
In these video you will see many examples of how to create fractions from repeating decimals.
.222 or .1666 and .2323 are all examples of repeating decimals. They are also called recurring decimals. How do you change these repeating decimals to fractions?
Example Number 1
Write .666 as a fraction.
First, look at the numerator rules. The problem only has one repeating number so write the number which is 6
Numerator = 6
Now we have the denominator
There is only one repeating number so the denominator equals 9
Denominator = 9
Final answer 6/9 which can be reduced to 2/3
Example Number 2
Follow the numerator rules. The decimal is mixed and 4 is the non-repeating number
The first digit will be 4
Now take the difference between repeating 7 and non-repeating number 4 =3
Combine these and the numerator equals 43
Now the denominator
The problem has one repeating number which is 7 so this will be a 9
Next, add a 0 for the non-repeating number 4
Combine these and you have 90 The 0 always goes to the right of the 9
Final answer equals 43/90
Example problem 3
Numerator has one non-repeating and two repeating numbers.
The non-repeating number 2 will be the first digit
Next, take the difference between the repeating and non-repeating number.
34 - 2 = 32
Numerator = 232
Now the denominator
You have two repeating numbers, 34 so you will have a 99
Next, you have one non-repeating number 2, so write a 0
Combine these and this equals 990
Final answer = 232/990