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Class 10MathematicsReal NumbersDecimal expansion of rational numbersExpertLevel 19
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If (q=2^r5^s) and (\frac{p}{q}) is in lowest form, what is the minimum (k) to write the decimal as (\frac{N}{10^k})?

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Answer and explanation

Correct answer: (\max(r,s))

To form (10^k=2^k5^k), both powers must reach at least the larger exponent. Therefore the minimum (k=\max(r,s)).

Related tags

General-FormulaPowers-Of-10Terminating-DecimalExpert

Frequently asked questions

What is the correct answer to this question?

(\max(r,s))

Why is this the correct answer?

To form (10^k=2^k5^k), both powers must reach at least the larger exponent. Therefore the minimum (k=\max(r,s)).

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?
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