Question

Write 1.12121212121... as a mixed number

Answer 1

So the mixed number rule should help. Since we have a whole number, which is 1, then it stays like that. The "12121212121..." means that it repeats the number, 12, many times, meaning that the denominator is 99 (12 = 99 for the denominator.) We would get 12/99, but the thing is that we can simplify this fraction (we divide the numerator and the denominator 3 times for this fraction), giving us 4/33.

Hope this helped!

Nate

Answer 2

Let x = 1.121212...

Then 100x = 112.121212...

Then 100x - x = 112.121212... - 1.121212, or 99x = 111, so x = 111/99 = 37/33 = 1 + 4/33.