What type of decimal expansion will ( \frac{13}{28} ) have?

Non-terminating recurring

A fraction in lowest terms has a terminating decimal expansion precisely when its denominator contains no prime factors other than 2 and 5. If another prime factor occurs, division continues indefinitely and produces a repeating pattern. Therefore, the denominator must be factored after confirming that no common factor remains between numerator and denominator.

For \(13/28\), the fraction is already in simplest form because 13 does not divide 28. Factor the denominator as \(28=2^2\times7\). The factor 7 is different from 2 and 5, so the decimal expansion cannot terminate. Since the fraction is rational, its infinite decimal digits must repeat rather than become non-repeating. Thus the correct classification is non-terminating recurring, option B. Option A would be correct only if the denominator had factors 2 and 5 alone.

This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.