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Class 10MathematicsReal NumbersDecimal expansion of rational numbersMediumLevel 21
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If a fraction in lowest form has denominator (320), after at most how many places will its decimal expansion terminate?

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Answer and explanation

Correct answer: (6) places

Step 1: (320=2^6\times5). Step 2: The denominator has only (2) and (5), so the decimal terminates. Step 3: The larger exponent is (6), so it terminates within (6) places.

Related tags

Decimal PlacesTerminating DecimalsPrime FactorsExam Practice

Frequently asked questions

What is the correct answer to this question?

(6) places

Why is this the correct answer?

Step 1: (320=2^6\times5). Step 2: The denominator has only (2) and (5), so the decimal terminates. Step 3: The larger exponent is (6), so it terminates within (6) places.

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?
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