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What is the value of $0.1 \overline{2}$ ? (Only the 2 repeats.)

Class 9Decimal Expansions of Real NumbersNumber Systems

A $\frac{12}{99}$
B $\frac{12}{90}$
C $\frac{4}{33}$
D $\frac{11}{90}$

Step-by-Step Solution

x = 0.1222

…,

10 x = 1.222

…,

100 x = 12.222

….

90 x = 11, x = 11/90

. (12/99 = 4/33 is 0.1212…, a different number.)

Answer: D)

\frac{11}{90}

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