For example, all integers are rational numbers because every integer can be written in the form of p / q as follows:

1 =11,-1 =-11and100 =1001

More rational numbers are 2/3, 4/5, 6/7, which are not integers but they are rational because they are in the form of p/q.

Non recurring and non terminating decimals are not rational numbers. These are those decimals, that keep on getting more digits after the decimal point, and they show no repetition of a single or a set of digits after the decimal point. For example, square root of 2 is not a rational number because it results in a decimal number that keeps going on without showing any repetition in digits.

Similarly √3, √5, √6, √7 .. are not rational numbers. Square roots of perfect squares, and some other square roots which result in a terminating decimal are rational numbers. For example √100 and √9 are rational numbers, and so are √1.21, √2.25 and √1.69.

Zero is a rational number, because zero divided by 1 is 0, and 0/1 is in the form of p/q.

All those numbers which have a zero in their denominator, for example, 1/0, 100/0, -1/0 are not rational numbers because dividing by zero does not give a definite result.

Non recurring and non terminating decimals are not rational numbers. These are those decimals, that keep on getting more digits after the decimal point, and they show no repetition of a single or a set of digits after the decimal point. For example, square root of 2 is not a rational number because it results in a decimal number that keeps going on without showing any repetition in digits.

Similarly √3, √5, √6, √7 .. are not rational numbers. Square roots of perfect squares, and some other square roots which result in a terminating decimal are rational numbers. For example √100 and √9 are rational numbers, and so are √1.21, √2.25 and √1.69.

Zero is a rational number, because zero divided by 1 is 0, and 0/1 is in the form of p/q.

All those numbers which have a zero in their denominator, for example, 1/0, 100/0, -1/0 are not rational numbers because dividing by zero does not give a definite result.