That reminds me with my 4th grade year. I used an old 4 func. calculator to get the circumference of a circle. The calculator never came up with a whole number answer. Unlikely calculators of the day don't, why ? Because they are capable of doing some approximation and fractions work. The idea is, we humans use numbers of a base of 10 digits, and each digit then may have a place value varying from 0x10^index of digit from the decimal point to 1x10^index of digit from the decimal point (computers use binary or 2 digits, which are 1 and... well a digit place can't value 2 as it can't value 10 in our numbers). Then, 123 = 1x10(^exponent)2 +2x10^1 +3x10^0 =100 + 20 + 3.
The problem here is that you don't have a digit which equals 1/9 of 10. That results in an infinite number of digits because with each 1 you add to before the decimal point, the value becomes closer to 1/9 , yet it doesn't equal 1/9 which needs a digit wich doesn't exist between 0 and 10. When using a fraction you put your own base represented in the denomenator which is 9. So if you use a decimal number (which can be represented in a fraction like this ?/1x10^decimal places) no digit can represent a 1/9 except 0.1111.../10.
To sum that in few words, 0.1111... =1/9 but
0.1111... is too long to read till it reaches an exact value of 1/9 since it's of an infenite long
NOTE: please don't take this too seriously when reading (I should've said that at the beggining) cuz I wrote that out of my own mind and ideas. It's somehow similar ofcourse to that wiki article but my post isn't in exact scientific words. I'm still a high school grader anyway.