In simplest form, what type of decimal expansion will 96/180 have?

Non-terminating recurring decimal

A rational number has a terminating decimal only when, after reducing the fraction completely, the denominator has no prime factors other than 2 and 5. If any other prime factor remains in the denominator, the decimal continues forever in a repeating pattern. This rule helps us identify the type without needing to perform a long division. It also shows why the phrase “in simplest form” is important: common factors may hide the actual denominator structure.

The greatest common divisor of 96 and 180 is 12. Therefore, \(96/180=8/15\). The denominator 15 factors as \(3\times5\), so it contains the prime factor 3 as well as 5. Hence the decimal does not terminate; because \(8/15\) is rational, its continuing digits must repeat. Thus option B, non-terminating recurring decimal, is correct. It is not non-recurring, since non-terminating non-recurring decimals are irrational numbers.

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