Question

I need help with #4 a-d

Answer 1

a repeating decimal is placed over 9's instead of 0's.   for example: 0.23 = $\frac{23}{100}$, but 0.232323... = $\frac{23}{99}$

a) x = 0.121212

b) 100(x) = 100(0.121212)

    100x  = 12.1212

c)  100x = 12.1212

-          x =   0.1212

     99x  =  12

         x  = $\frac{12}{99}$

d) -2$\frac{12}{99}$  = -2$\frac{4}{33}$ when simplified

The number is rational becase it has a repeating decimal