How to find terminating and non …

Terminating decimals: Terminating decimals are those numbers which come to an end after few repetitions after decimal point.

Example: 0.5, 2.456, 123.456, etc. are all examples of terminating decimals.
(i) <nobr aria-hidden="true">1/2</nobr> is a rational fraction of form <nobr aria-hidden="true">p/q</nobr>. When this rational fraction is converted to decimal it becomes 0.5, which is a terminating decimal fraction.

Non terminating decimals: Non terminating decimals are those which keep on continuing after decimal point (i.e. they go on forever). They don’t come to end or if they do it is after a long interval.

For example:

π = (3.141592653589793238462643383279502884197169399375105820974.....) is an example of non terminating decimal as it keeps on continuing  after decimal point.

(i)  <nobr aria-hidden="true">1/3</nobr>is a rational fraction of form <nobr aria-hidden="true">p/q</nobr>. When we convert this rational fraction into decimal, it becomes 0.333333… which is a non terminating decimal.