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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 19
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If (\frac{n}{180}) has a terminating decimal expansion and the fraction is not necessarily in lowest form, what factor must (n) contain at minimum?

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Answer and explanation

Correct answer: (3^2)

Step 1: (180=2^2\cdot 3^2\cdot 5). Step 2: For a terminating decimal, (3^2) must cancel completely from the denominator. So (n) must contain (3^2). Step 3: Focus on removing denominator primes other than (2) and (5).

Related tags

Terminating-DecimalMinimum-FactorPrime-FactorisationHard

Frequently asked questions

What is the correct answer to this question?

(3^2)

Why is this the correct answer?

Step 1: (180=2^2\cdot 3^2\cdot 5). Step 2: For a terminating decimal, (3^2) must cancel completely from the denominator. So (n) must contain (3^2). Step 3: Focus on removing denominator primes other than (2) and (5).

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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