Question

Express 0.9666... as a quotient of two integers

Answer 1

let x = 0.9666....

create 2 equations by multiplying by 100 and 10

then subtract them


100x = 96.66666
10x = 9.666....
-----------------
90x = 87

now just solve for x and simplify

Answer 2

\[\frac{87}{90}=\frac{29}{30} \]