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Subjects
Class 10MathematicsReal NumbersDecimal expansion of rational numbersMediumLevel 21
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What is the simplest fractional form of (0.\overline{18})?

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Answer and explanation

Correct answer: (\frac{2}{11})

Step 1: The repeating block is (18), so (0.\overline{18}=\frac{18}{99}). Step 2: (\frac{18}{99}=\frac{2}{11}). Step 3: The number of (9)s in the denominator equals the number of repeating digits.

Related tags

Recurring DecimalFraction ConversionRational Numbers

Frequently asked questions

What is the correct answer to this question?

(\frac{2}{11})

Why is this the correct answer?

Step 1: The repeating block is (18), so (0.\overline{18}=\frac{18}{99}). Step 2: (\frac{18}{99}=\frac{2}{11}). Step 3: The number of (9)s in the denominator equals the number of repeating digits.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Decimal expansion of rational numbers.

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  2. 2What type of decimal expansion does (\frac{5}{6}) have?
  3. 3Under what condition does (\frac{p}{q}) have a terminating decimal expansion when the fraction is in lowest form?
  4. 4After reducing (\frac{15}{40}), what type of decimal expansion will it have?
  5. 5After at most how many decimal places will the decimal expansion of (\frac{7}{16}) terminate?
  6. 6Choose the correct statement about the decimal expansion of (\frac{11}{45}).
  7. 7Which of the following fractions will give a terminating decimal?
  8. 8Which of the following fractions will give a non-terminating recurring decimal?
  9. 9When (0.75) is written as a rational number, which form is obtained?
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