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Class 10MathematicsReal NumbersDecimal expansion of rational numbersExpertLevel 19
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If (n) is the smallest positive integer for which (\frac{n}{2^2\cdot 3^4\cdot 5\cdot 13}) has a terminating decimal, what is (n)?

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Answer and explanation

Correct answer: (1053)

For a terminating decimal, (3^4) and (13) must cancel completely, so (n=3^4\cdot 13=1053). For the least value, cancel only the unwanted prime factors.

Related tags

Minimum-FactorTerminating-ConditionExpert-McqReal-Numbers

Frequently asked questions

What is the correct answer to this question?

(1053)

Why is this the correct answer?

For a terminating decimal, (3^4) and (13) must cancel completely, so (n=3^4\cdot 13=1053). For the least value, cancel only the unwanted prime factors.

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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