Official papers

Official 2023 Paper 2 · Q15

Paper 2Algebra

The base 10 number 0.038410.03841 has the value

0×10−1+3×10−2+8×10−3+4×10−4+1×10−5=0.03841.0\times10^{-1}+3\times10^{-2}+8\times10^{-3}+4\times10^{-4}+1\times10^{-5}=0.03841.

Similarly, the base 2 number 0.011010.01101 has the value

0×2−1+1×2−2+1×2−3+0×2−4+1×2−5=1332.0\times2^{-1}+1\times2^{-2}+1\times2^{-3}+0\times2^{-4}+1\times2^{-5}=\frac{13}{32}.

What is the value of the recurring base 2 number 0.0˙011˙=0.001100110011…0.\dot{0}01\dot{1}=0.001100110011\ldots?

A13\frac13
B15\frac15
C115\frac1{15}
D215\frac2{15}
E415\frac4{15}
F316\frac3{16}
G516\frac5{16}
H631\frac6{31}

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