After how many decimal places will 72/(2^3 × 3^2 × 5^5) terminate?
Answer and explanation
Correct answer: 5
First reduce the fraction before applying the decimal-expansion rule. Since 72 = 2^3 × 3^2, the numerator cancels completely with the factors 2^3 × 3^2 in the denominator. Thus 72/(2^3 × 3^2 × 5^5) = 1/5^5 = 1/3125. To express this with a denominator that is a power of 10, multiply numerator and denominator by 2^5: 1/5^5 = 2^5/10^5 = 32/100000 = 0.00032. The decimal therefore ends after five digits to the right of the decimal point. Option C is correct. Options A and B use smaller exponents without justification, while option D is false because the reduced denominator contains only the prime factor 5, so the decimal is terminating.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
First reduce the fraction before applying the decimal-expansion rule. Since 72 = 2^3 × 3^2, the numerator cancels completely with the factors 2^3 × 3^2 in the denominator. Thus 72/(2^3 × 3^2 × 5^5) = 1/5^5 = 1/3125. To express this with a denominator that is a power of 10, multiply numerator and denominator by 2^5: 1/5^5 = 2^5/10^5 = 32/100000 = 0.00032. The decimal therefore ends after five digits to the right of the decimal point. Option C is correct. Options A and B use smaller exponents without justification, while option D is false because the reduced denominator contains only the prime factor 5, so the decimal is terminating.
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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