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Class 10MathematicsReal NumbersDecimal expansion of rational numbersMediumLevel 6
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Choose the correct statement about the set {x ∈ ℚ : x has a terminating decimal expansion}.

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Answer and explanation

Correct answer: It is infinite

There are infinitely many rational numbers with terminating decimal expansions. For example, 1/2 = 0.5, 1/4 = 0.25, 3/10 = 0.3, and every positive integer has a terminating decimal representation. More generally, numbers such as 1/10, 1/100, 1/1000, and so on are all distinct members. Therefore, the set is infinite, so option C is correct.

Related tags

SetsInfinite SetRational NumbersTerminating DecimalsDecimal Expansion Of Rational NumbersReal NumbersChapter 1 Real NumbersMathematics

Frequently asked questions

What is the correct answer to this question?

It is infinite

Why is this the correct answer?

There are infinitely many rational numbers with terminating decimal expansions. For example, 1/2 = 0.5, 1/4 = 0.25, 3/10 = 0.3, and every positive integer has a terminating decimal representation. More generally, numbers such as 1/10, 1/100, 1/1000, and so on are all distinct members. Therefore, the set is infinite, so option C 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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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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