What fraction is equal to (0.\overline{2})?
Answer and explanation
Correct answer: \(\frac{2}{9}\)
Let \(x=0.\overline{2}=0.222\ldots\). Multiplying by 10 gives \(10x=2.222\ldots\). Subtracting the first equation from the second gives \(9x=2\), so \(x=\frac{2}{9}\). Therefore, option A is correct. Exam tip: a decimal with one repeating digit, such as \(0.\overline{a}\), equals \(\frac{a}{9}\), not \(\frac{a}{10}\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{2}{9}\)
Why is this the correct answer?
Let \(x=0.\overline{2}=0.222\ldots\). Multiplying by 10 gives \(10x=2.222\ldots\). Subtracting the first equation from the second gives \(9x=2\), so \(x=\frac{2}{9}\). Therefore, option A is correct. Exam tip: a decimal with one repeating digit, such as \(0.\overline{a}\), equals \(\frac{a}{9}\), not \(\frac{a}{10}\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
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