17. Which of these is equal to $0 . \dot{8}+0.07$ ?
A $0.8 \dot{7}$
B 0.88
C $0.9 \dot{5}$
D $0.9 \dot{6}$
E $0.9 \dot{8}$
17. D It may be shown that $0 . \dot{1}=\frac{1}{9}$. So $0 . \dot{8}=\frac{8}{9}$ and $0.0 \dot{7}=\frac{7}{90}$.
Therefore $0 . \dot{8}+0.0 \dot{7}=\frac{8}{9}+\frac{7}{90}=\frac{80}{90}+\frac{7}{90}=\frac{87}{90}=\frac{29}{30}$. Now $\frac{29}{3}=9+\frac{2}{3}=9+0 . \dot{6}=9 . \dot{6}$. So $\frac{29}{30}=0.9 \dot{6}$. Hence $0 . \dot{8}+0.0 \dot{7}=0.9 \dot{6}$.
(It is left as an exercise to the reader to prove the assertion in the first sentence.)