What a fraction to 10.121212?

Answer 1

If the 12 repeats forever then here is how you can convert repeating decimals. Set x = the number, so x = 10.12121212...., next count the number of repeating digits and multiply both sides by ten raised to that number. There are 2 digits in the repeating pattern, so multiply by 10^2 = 100. so we have 100x = 1012.12121212..... Note that since it repeats forever, you can line up the digits.

Now subtract: 100x - x = (1012.12121212...) - (10.12121212...) ----> 99x = 1002.000000, therefore x = 1002/99. We can simplify by factoring out a 3 from numerator and denominator: 334/33. As a mixed number it is 10 4/33.