Follow these rules for changing a recurring decimal to a fraction.

Changing a repeating decimal back to a fraction

Rules:

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.

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

.4777

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

.2343434

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