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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 19
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For (\frac{a}{2^3\cdot 5^2\cdot 13}) to have a terminating decimal, what factor must (a) contain at minimum?

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Answer and explanation

Correct answer: (13)

Step 1: The denominator contains (2), (5), and (13). Step 2: For a terminating decimal, (13) must not remain in the reduced denominator. So (a) must contain the factor (13). Step 3: Powers of (2) and (5) may remain, but other prime factors must cancel.

Related tags

Terminating-ConditionPrime-FactorisationReal-NumbersHard-Mcq

Frequently asked questions

What is the correct answer to this question?

(13)

Why is this the correct answer?

Step 1: The denominator contains (2), (5), and (13). Step 2: For a terminating decimal, (13) must not remain in the reduced denominator. So (a) must contain the factor (13). Step 3: Powers of (2) and (5) may remain, but other prime factors must cancel.

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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