Answer: 21/99
Work Shown:
x = 0.212121...
100x = 21.212121....
Subtract the equations straight down. This means we subtract the left hand sides together, and the right hand sides are handled separately.
- Left hand sides: 100x-x becomes 99x
- Right hand sides: 21.212121.... - 0.212121... becomes 21
After those sets of subtractions, we are left with 99x = 21.
This solves to x = 21/99 when dividing both sides by 99 to isolate x.
Therefore, 21/99 = 0.212121...