Which rational number is equivalent to 3.90 with the .90 repeating?

Question

A. 3/90
B. 39/10
C. 35/9
D. 43/11
EXPLAIN PLZ

Answer 1

let x = 3.909090...
multiply by 100 , (because I have 2 digits repeating, thus 2 zeros in 100, had there been 3 digits repeating, I would have mulitplied by 1000)

100x = 390.909090...

subtract the original:
99x = 390.9090... - 3.909090..
99x = 387
x = 387/99 = 43/11

Answer 2

thanks Reiny :))