Question

Let x= p/q be a rational number, such that the prime factorisation of q is not of the form $2^m{5}^n$, where n, m are non-negative integers. Then, x has a decimal expansion which is ___.

• A. Non-terminating repeating (recurring)
• B. Terminating non-repeating (non-recurring)
• C. Real Integer
• D. None of these

Answer 1

The correct option is A Non-terminating repeating (recurring)

A decimal is terminating only when the denominators can be prime factored in the form of $2^m{5}^n$. If the denominator has any other prime factor then the decimal becomes non-terminating and repeating.