If ( \frac{p}{q} ) is in simplest form and (q=2^6\times5^9), what is the maximum number of decimal places in the terminating decimal?
Answer and explanation
Correct answer: (9)
The denominator is \\(2^6\times5^9\\). A terminating decimal is formed by making the denominator a power of 10, so the powers of 2 and 5 must be made equal. There are six factors of 2 and nine factors of 5; therefore, multiply by \\(2^3\\) to obtain \\(2^9\times5^9=10^9\\). This requires at most nine decimal places.
The same conclusion follows from the standard rule: the maximum number of places is the larger exponent in the simplified denominator. Here, \\(\max(6,9)=9\\), so option B is correct. The value 15 would incorrectly add the exponents. Although a special numerator may cancel factors and produce fewer places, the maximum possible number remains nine.
Frequently asked questions
What is the correct answer to this question?
(9)
Why is this the correct answer?
The denominator is \\(2^6\times5^9\\). A terminating decimal is formed by making the denominator a power of 10, so the powers of 2 and 5 must be made equal. There are six factors of 2 and nine factors of 5; therefore, multiply by \\(2^3\\) to obtain \\(2^9\times5^9=10^9\\). This requires at most nine decimal places.
The same conclusion follows from the standard rule: the maximum number of places is the larger exponent in the simplified denominator. Here, \\(\max(6,9)=9\\), so option B is correct. The value 15 would incorrectly add the exponents. Although a special numerator may cancel factors and produce fewer places, the maximum possible number remains nine.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
