Number Systems

A rational number is of the form of p/q, where p and q are integers and the denominator is not equal to zero. The decimal expansion of rational number is either terminating or non-terminating recurring. A number is called irrational number, if it cannot be written in the form of p/q, where p and q are integers and q is not equal to zero. The decimal expansion of an irrational number is non-terminating non-recurring. Real Numbers are collection of all rational and irrational numbers. There is a real number corresponding to each point on the number line and vice versa. The sum, difference and product of a rational and an irrational number are always an irrational number. Also, when an irrational number is divided by a rational number then the quotient is an irrational number. For any non-zero real number ‘a’ and a positive integer ‘n’, we define If a, b are any real numbers and m, n are any positive integers, then The set of natural numbers along with zero is called the set of whole numbers. W = {0, 1, 2, 3…} Number line is a straight line on which all the numbers can be represented. The set of positive and negative numbers is called integers. I or Z = {-3, -2, -1, 0, 1, 2, 3…}

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