Question

Find fractional notation for the infinite sum (these are geometric series) 0.1919191919

Answer 1

Let x = 0.191919...
Now, we want to find some sort of relationship with x and 0.191919...

If we multiply x by 100, we get:

`100x = 19.19191919...`

Now, it's clear that the decimal places will cancel when we subtract it:

`100x - x = 19.19191919... - 0.19191919...`

`99x = 19`

Solving for x, we get:

`x = (19)/(99)`