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Class 10MathematicsReal NumbersDecimal expansion of rational numbersEasyLevel 20
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Assertion: If (\frac{p}{q}) is in lowest form and (q) has a factor (7), the decimal will not terminate. Reason: For a terminating decimal, the denominator in lowest form must be made only of (2) and (5). Choose the correct option.

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Answer and explanation

Correct answer: Both assertion and reason are true, and the reason explains the assertion

Step 1: For a terminating decimal, the denominator in lowest form must be made only of (2) and (5). Step 2: If (7) remains, this condition fails and the decimal will not terminate. Step 3: The reason correctly explains the assertion, so the first option is correct.

Related tags

Real NumbersAssertion ReasonDenominator FactorClass 10

Frequently asked questions

What is the correct answer to this question?

Both assertion and reason are true, and the reason explains the assertion

Why is this the correct answer?

Step 1: For a terminating decimal, the denominator in lowest form must be made only of (2) and (5). Step 2: If (7) remains, this condition fails and the decimal will not terminate. Step 3: The reason correctly explains the assertion, so the first option is correct.

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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