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Class 10MathematicsReal NumbersDecimal expansion of rational numbersMediumLevel 21
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The denominator of a rational number in lowest form is (2^3 \times 5^2 \times 7). Choose the correct statement about its decimal expansion.

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Answer and explanation

Correct answer: Non-terminating repeating

Step 1: A rational number has a terminating decimal only when the denominator in lowest form has prime factors only (2) and (5). Step 2: Here the denominator also contains (7), so the decimal will not terminate, but since the number is rational, it will repeat. Step 3: In exams, always reduce the fraction first and then check the prime factors of the denominator.

Related tags

Real NumbersDecimal ExpansionRational NumbersTerminating DecimalRepeating Decimal

Frequently asked questions

What is the correct answer to this question?

Non-terminating repeating

Why is this the correct answer?

Step 1: A rational number has a terminating decimal only when the denominator in lowest form has prime factors only (2) and (5). Step 2: Here the denominator also contains (7), so the decimal will not terminate, but since the number is rational, it will repeat. Step 3: In exams, always reduce the fraction first and then check the prime factors of the denominator.

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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