Home › Karnataka SSLC (Class 10) › Mathematics › Real Numbers › A rational number $\dfrac{p}{q}$ (in lowest term…
A rational number $\dfrac{p}{q}$ (in lowest terms) has a terminating decimal expansion if and only if the prime factorisation of $q$ is of the form
A$3^n \times 7^m$
B$2^n \times 3^m$
Cany product of primes
D$2^n \times 5^m$
Answer & Solution
Correct answer: D. $2^n \times 5^m$
1. A decimal terminates only when the denominator's primes are 2 and/or 5.
2. So $q$ must be of the form $2^n \times 5^m$ (n, m ≥ 0).
3. e.g. $3/8 = 3/2^3 = 0.375$ terminates, but $1/3$ does not.
_Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch8 'Real Numbers', §8.4 (decimal expansions)_
Related questions
The largest number that divides both 60 and 96 exactly (their HCF) isThe decimal expansion of an irrational number isThe sum of a rational number and an irrational number is alwaysThe product of the HCF and LCM of the numbers 8 and 20 isThe prime factorisation of 140 isUsing Euclid's algorithm, the HCF of 96 and 404 isIf the HCF of two numbers is 9 and their LCM is 90, and one number is 18, the other numberThe LCM of 12 and 18 is