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Class 10MathematicsReal NumbersDecimal expansion of rational numbersMediumLevel 20
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Why will the decimal expansion of (\frac{9}{28}) not terminate?

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Answer and explanation

Correct answer: Because the denominator also contains (7)

Step 1: (28=2^2\times7). Step 2: The reduced denominator contains (7), which is not (2) or (5). Step 3: If another prime factor remains, the decimal is non-terminating recurring.

Related tags

Non Terminating RecurringPrime FactorsRational Numbers

Frequently asked questions

What is the correct answer to this question?

Because the denominator also contains (7)

Why is this the correct answer?

Step 1: (28=2^2\times7). Step 2: The reduced denominator contains (7), which is not (2) or (5). Step 3: If another prime factor remains, the decimal is non-terminating recurring.

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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