When 0.0375 is written in lowest fraction form, what is the prime factorisation of the denominator?
Answer and explanation
Correct answer: 2⁴ · 5
The governing concept is converting a terminating decimal to lowest fractional form and then prime-factorising the reduced denominator. Since 0.0375 has four decimal places, write it as 375/10000. Divide numerator and denominator by their greatest common divisor, 125: 375 ÷ 125 = 3 and 10000 ÷ 125 = 80. Thus 0.0375 = 3/80. Now factor the denominator: 80 = 8 × 10 = 2³ × (2 × 5) = 2⁴ × 5. Therefore option B is correct. Option A misses one factor of 2, while options C and D introduce an extra factor of 5 and do not represent the prime factorisation of 80. Reduction before factorisation is important.
Frequently asked questions
What is the correct answer to this question?
2⁴ · 5
Why is this the correct answer?
The governing concept is converting a terminating decimal to lowest fractional form and then prime-factorising the reduced denominator. Since 0.0375 has four decimal places, write it as 375/10000. Divide numerator and denominator by their greatest common divisor, 125: 375 ÷ 125 = 3 and 10000 ÷ 125 = 80. Thus 0.0375 = 3/80. Now factor the denominator: 80 = 8 × 10 = 2³ × (2 × 5) = 2⁴ × 5. Therefore option B is correct. Option A misses one factor of 2, while options C and D introduce an extra factor of 5 and do not represent the prime factorisation of 80. Reduction before factorisation is important.
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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