Express 0.23̄ as a fraction in its lowest terms.

Question 29

MediumOriginal question

Express $0.2\overline{3}$ as a fraction in its lowest terms.

\frac{7}{33}

Correct answerYour answer

\frac{23}{100}

Correct answerYour answer

\frac{23}{99}

Correct answerYour answer

\frac{7}{30}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Only the 3 repeats. For a mixed recurring decimal: (all digits − non-repeating digits) ÷ (one 9 per repeating digit, one 0 per non-repeating digit).
$0.2\overline{3} = \frac{23 - 2}{90} = \frac{21}{90}$ .
Simplify: $\frac{21}{90} = \frac{7}{30}$ .

Worth noting

$\frac{23}{99}$ is $0.\overline{23}$ , where both digits repeat, and $\frac{21}{99} = \frac{7}{33}$ uses 99 in place of 90. Check: $7 \div 30 = 0.2333\ldots$

Concept: Converting a mixed recurring decimal to a fraction
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsFractions and decimals

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Ten questions from Simplification & Approximation, at your own pace.

Express 0.23‾0.2\overline{3}0.23 as a fraction in its lowest terms.

Explanation

Express $0.2\overline{3}$ as a fraction in its lowest terms.