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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 19
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If a rational number has a non-terminating recurring decimal expansion, which statement about its denominator in lowest form is correct?

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Answer and explanation

Correct answer: The denominator has at least one prime factor other than (2) and (5)

Step 1: A non-terminating decimal of a rational number is recurring. Step 2: This happens when the reduced denominator has at least one prime factor other than (2) and (5). So option (C) is correct. Step 3: (2) or (5) may also be present, but some other prime must remain.

Related tags

Recurring-DecimalDenominator-ConditionReal-NumbersTheory

Frequently asked questions

What is the correct answer to this question?

The denominator has at least one prime factor other than (2) and (5)

Why is this the correct answer?

Step 1: A non-terminating decimal of a rational number is recurring. Step 2: This happens when the reduced denominator has at least one prime factor other than (2) and (5). So option (C) is correct. Step 3: (2) or (5) may also be present, but some other prime must remain.

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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  1. 1What type of decimal expansion will the rational number (\frac{3}{8}) have?
  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?
  10. 10If the denominator of a fraction in lowest form is (2^3\times5^2), after at most how many decimal places will its decimal expansion terminate?
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