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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 21
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If (\frac{a}{2^2\cdot 3\cdot 5\cdot 19}) is to have a terminating decimal, what factor must (a) contain at minimum?

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Answer and explanation

Correct answer: (57)

Step 1: The denominator contains (2), (5), (3), and (19). Step 2: For a terminating decimal, (3) and (19) must cancel. So the minimum factor is (3\cdot 19=57). Step 3: Only (2) and (5) may remain in the denominator.

Related tags

Minimum-FactorTerminating-DecimalPrime-FactorisationHard

Frequently asked questions

What is the correct answer to this question?

(57)

Why is this the correct answer?

Step 1: The denominator contains (2), (5), (3), and (19). Step 2: For a terminating decimal, (3) and (19) must cancel. So the minimum factor is (3\cdot 19=57). Step 3: Only (2) and (5) may remain in the denominator.

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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