The following procedure is for converting a general repeating decimal, that is, one which does not start repeating straight away. Until you become expert at this I suggest you do this in two stages (using c and d separately). Suppose there are c digits after the decimal place where the digits are non-repeating, and then you get a repeating pattern of a string of d digits. Then the numerator is the old original string including one lot of the repeated digits minus the original string with none of the repeating digits. The denominator is 10^c*(10^d - 1), which is a string of d 9s followed by c 0s.
Example
123.26159159… There are 2 digits, "26", after the decimal point before the repeats kick in so c = 2, and the repeating string "159" is 3 digits long so d = 3.
So the numerator of the fraction is 12326159 – 12326 = 12313833
and the denominator is 99900
Therefore the fraction is 12313833/99900.
0.2 a repeating decimal into a fraction = 2/9
Just have a go.
sexx
0.999 repeating = 1 (the integer).
123/999 = 41/333
0.2 a repeating decimal into a fraction = 2/9
Just have a go.
sexx
0.999 repeating = 1 (the integer).
123/999
998/999
998/999
You can round the decimal fraction to a suitable level of accuracy. Alternatively, you can convert the number to a rational fraction.
123/999 = 41/333
5/36 = 0.138888(repeating)
To convert a fraction to a decimal, divide the top number by the bottom number.
To convert a repeating decimal to a fraction, let x = -6.8. Multiply the repeating decimal by a power of 10 to eliminate the repeating part. Therefore, 10x = -68.8888.... Subtract the original equation from this to get 9x = -75, which simplifies to x = -75/9. Thus, the fraction form of -6.8 repeating decimal is -75/9.