Question

.1515 repeat, I get 303/2000 and divide it to get the .1515 repeat, but in my book, it says the answer is 5/33, how is that

Answer 1

if
n = .15151515...
100n = 15.15151515...

so,

99n = 15
n = 15/99 = 5/33

Any group of n digits which repeats is the string of digits divided by a string of 9's of the same length:

.333333 = 3/9
.15151515 = 15/99
.67836783... = 6783/9999

and so on

Answer 2

how do you get the 99n? im sorry but I am really confused

Answer 3

the usual way
subtract n from 100n to get 99n
look above to see that

15.151515...
-0.151515...
= 15