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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 21
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What type of decimal expansion will (\frac{154}{2\cdot 5^3\cdot 7\cdot 11}) have?

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Answer and explanation

Correct answer: Terminating after (3) places

Step 1: (154=2\cdot 7\cdot 11). Step 2: After cancelling (2\cdot 7\cdot 11), the denominator becomes (5^3). So the decimal terminates after (3) places. Step 3: Extra factors may cancel with the numerator, so reduce first.

Related tags

CancellationTerminating-DecimalPrime-FactorisationReal-Numbers

Frequently asked questions

What is the correct answer to this question?

Terminating after (3) places

Why is this the correct answer?

Step 1: (154=2\cdot 7\cdot 11). Step 2: After cancelling (2\cdot 7\cdot 11), the denominator becomes (5^3). So the decimal terminates after (3) places. Step 3: Extra factors may cancel with the numerator, so reduce first.

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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  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?
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  7. 7Which of the following fractions will give a terminating decimal?
  8. 8Which of the following fractions will give a non-terminating recurring decimal?
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