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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 20
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For (\frac{a}{2310}) to have a terminating decimal expansion, what factor must (a) contain at minimum?

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Answer and explanation

Correct answer: (231)

Step 1: (2310=2\cdot 3\cdot 5\cdot 7\cdot 11). Step 2: For a terminating decimal, (3), (7), and (11) must cancel from the denominator. So the minimum factor is (3\cdot 7\cdot 11=231). Step 3: (2) and (5) may remain, but other prime factors must not.

Related tags

Minimum-FactorTerminating-ConditionPrime-FactorisationAdvanced

Frequently asked questions

What is the correct answer to this question?

(231)

Why is this the correct answer?

Step 1: (2310=2\cdot 3\cdot 5\cdot 7\cdot 11). Step 2: For a terminating decimal, (3), (7), and (11) must cancel from the denominator. So the minimum factor is (3\cdot 7\cdot 11=231). Step 3: (2) and (5) may remain, but other prime factors must not.

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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  7. 7Which of the following fractions will give a terminating decimal?
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