If ( \frac{p}{q} ) is in simplest form and (q=2^5\times5^2), what is the maximum number of decimal places in the terminating decimal?
Answer and explanation
Correct answer: (5)
A fraction with denominator \\(2^5\times5^2\\) can be converted into a denominator that is a power of 10. To do this, the smaller power, \\(5^2\\), must be matched with two more factors of 5, while the two factors of 2 are already available. The resulting denominator is \\(2^5\times5^5=10^5\\). Hence the decimal can require at most five places.
The maximum is determined by the larger exponent, not by adding the exponents. Thus it is 5, which is option B. For example, multiplying numerator and denominator by \\(5^3\\) gives a denominator of \\(10^5\\). Some fractions may have fewer places because cancellation or trailing zeros can occur, but five is the greatest possible number under the stated denominator condition.
Frequently asked questions
What is the correct answer to this question?
(5)
Why is this the correct answer?
A fraction with denominator \\(2^5\times5^2\\) can be converted into a denominator that is a power of 10. To do this, the smaller power, \\(5^2\\), must be matched with two more factors of 5, while the two factors of 2 are already available. The resulting denominator is \\(2^5\times5^5=10^5\\). Hence the decimal can require at most five places.
The maximum is determined by the larger exponent, not by adding the exponents. Thus it is 5, which is option B. For example, multiplying numerator and denominator by \\(5^3\\) gives a denominator of \\(10^5\\). Some fractions may have fewer places because cancellation or trailing zeros can occur, but five is the greatest possible number under the stated denominator condition.
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.
