Find 0.12̄ + 0.12̄ as a fraction.

Question 37

HardOriginal question

Find $0.\overline{12} + 0.1\overline{2}$ as a fraction.

\frac{6}{25}

Correct answerYour answer

\frac{8}{33}

Correct answerYour answer

\frac{241}{990}

Correct answerYour answer

\frac{11}{45}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$0.\overline{12} = \frac{12}{99} = \frac{4}{33}$ (both digits repeat).
$0.1\overline{2} = \frac{12 - 1}{90} = \frac{11}{90}$ (only the 2 repeats).
LCM of 33 and 90 is 990: $\frac{120}{990} + \frac{121}{990} = \frac{241}{990}$ .

Worth noting

The two decimals look alike but are different: $0.121212\ldots$ and $0.122222\ldots$ . Treating both as $0.\overline{12}$ gives $\frac{8}{33}$ .

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