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Class 10MathematicsReal NumbersDecimal expansion of rational numbersMediumLevel 20
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Statement: If a fraction (\frac{p}{q}) in lowest form has (q=2^a5^b), then its decimal expansion will terminate. Choose the correct option.

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Answer and explanation

Correct answer: The statement is true

Step 1: For a terminating decimal, the reduced denominator must contain only (2) and (5). Step 2: (q=2^a5^b) exactly shows this form. Step 3: The numerator does not change the type once the fraction is in lowest form.

Related tags

Assertion ReasoningTerminating DecimalTheorem

Frequently asked questions

What is the correct answer to this question?

The statement is true

Why is this the correct answer?

Step 1: For a terminating decimal, the reduced denominator must contain only (2) and (5). Step 2: (q=2^a5^b) exactly shows this form. Step 3: The numerator does not change the type once the fraction is in lowest form.

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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10 more MCQs
  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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