Problem: Let D represent a repeating decimal. If P denotes the r figures of D which do not repeat themselves, and Q denotes the s figures which do repeat themselves, then the incorrect expression is:
Answer Choices:
A. D=.PQQQ⋯
B. 10rD=P.QQQ⋯
C. 10r+sD=PQ.QQQ⋯
D. 10r(10s−1)D=Q(P−1)
E. 10r⋅1028D=PQQ.QQQ⋯
Solution:
D=.PQQQ⋯=.a1⋯arb1⋯bsb1⋯bs⋯. So (A), (B), (C) and (E) are all correct choices. To check that (D) is incorrect, we have
10r+sD−10rD=PQ−P.∴10r(10s−1)D=P(Q−1).