A. To change repeating decimals of this pattern to fractions follow these steps:
1. To find the numerator, take the digits that are NOT repeating and subtract this value from these digits plus one more.
2. The first digit of the denominator is 9 followed by the same number of 0's as the number of non-repeating digits.
Ex [1] .12333... = ________(fraction)
a. The numerator is 123 - 12 = 111.
b. The denominator is 900.
c. The fraction is 111/900 which reduces to 37/300.
d. The answer is 37/300.
Ex [2] .2444... = _______(fraction)
a. The numerator is 24 - 2 = 22.
b. The denominator is 90.
c. The fraction is 22/90 which reduces to 11/45.
d. The answer is 11/45.
B. If the repeating digit is a 9, then the problem becomes easier:
1. Add 1 to the non repeating digits to get the decimal form of the answer.
Ex [1] .4999... =________(fraction).
a. Add 1 to 4 to get 5. The decimal form of the answer is .5. So the answer in a fraction is 1/2.
Ex [2] .74999...=________(fraction).
a. Add 1 to 74 to get 75. The decimal form of the answer is .75. So the answer in a fraction is 3/4.