Question

Negative 0.09 repeating as a fraction

Answer 1

We can use a clever trick to solve this problem.

Call the decimal x.  We see that:

x=-.09999...
and that:
100x=-9.9999...

Subtracting the second equation from the first, we see that:

99x=-9.9

Dividing by 99, we see that x=-.1.