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Class 10MathematicsReal NumbersDecimal expansion of rational numbersExpertLevel 21
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In the decimal expansion of (\frac{1}{2^7\cdot 5^3\cdot 41}), how many non-repeating digits appear before the recurring part?

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Answer and explanation

Correct answer: (7)

The factor (41) makes the decimal recurring, and the larger exponent of (2) and (5) is (7), giving the non-repeating start. In mixed denominators, the larger exponent gives the delay.

Related tags

PreperiodRecurring-DecimalDenominator-AnalysisExpert

Frequently asked questions

What is the correct answer to this question?

(7)

Why is this the correct answer?

The factor (41) makes the decimal recurring, and the larger exponent of (2) and (5) is (7), giving the non-repeating start. In mixed denominators, the larger exponent gives the delay.

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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