Question : $1.\overline{2} \times 0.\overline{03}$ =
Option 1: $0.\overline{04}$
Option 2: $0.0\overline{36}$
Option 3: $1.\overline{13}$
Option 4: $0.\overline{037}$
Correct Answer: $0.\overline{037}$
Solution :
Given: $1.\overline{2} \times 0.\overline{03}$
Fraction form of $1.\overline{2}= \left (1+\frac{2}{9} \right )=\frac{11}{9}$
Fraction form of $0.\overline{03}=\frac{3}{99} =\frac{1}{33}$
Now, $1.\overline{2} \times 0.\overline{03}=\frac{11}{9} \times \frac{1}{33}=\frac{1}{27}=\frac{1 \times37}{27 \times 37}=\frac{37}{999}=0.\overline{037}$
Hence, the correct answer is $0.\overline{037}$.
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