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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 21
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If (\frac{p}{q}) has a terminating decimal and is in lowest form, what can be said about the prime factors of (q^2)?

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Answer and explanation

Correct answer: Only (2) and (5) can occur

Step 1: For a terminating decimal, the reduced denominator (q) can contain only (2) and (5). Step 2: In (q^2), the powers of the same primes increase, but no new prime factor appears. Step 3: Powers may change, but the prime types do not.

Related tags

Terminating-DecimalPrime-FactorsDenominator-PropertyConceptual

Frequently asked questions

What is the correct answer to this question?

Only (2) and (5) can occur

Why is this the correct answer?

Step 1: For a terminating decimal, the reduced denominator (q) can contain only (2) and (5). Step 2: In (q^2), the powers of the same primes increase, but no new prime factor appears. Step 3: Powers may change, but the prime types do not.

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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