Answer:
[tex]\text{A. }25/33,\\\text{B. }1/3, \\\text{C. }1/33, \\\text{D. }25/9[/tex]
Step-by-step explanation:
Recall that [tex]\frac{x}{9}=0.\overline{x}[/tex] for [tex]x\in (1, 8)[/tex]. If multiple digits are repeating, increase the number of nines in the denominator as applicable.
Therefore, we have:
Part A:
"75" is repeating:
[tex]\rightarrow \frac{75}{99}=\boxed{\frac{25}{33}}[/tex]
Part B:
"3" is repeating:
[tex]\rightarrow \frac{3}{9}=\boxed{\frac{1}{3}}[/tex]
Part C:
"03" is repeating:
[tex]\rightarrow \frac{03}{99}=\frac{3}{99}=\boxed{\frac{1}{33}}[/tex]
Part D:
"7" is repeating, but there is a terminating decimal 2.0 with it ([tex]2.\overline{7}=2.0+0.\overline{7}[/tex]):
[tex]2+\frac{7}{9}=\frac{18}{9}+\frac{7}{9}=\boxed{\frac{25}{9}}[/tex]
