Number System: Overview, Questions, Preparation

What is Number System?

The number system is divided into two parts:

1. Imaginary numbers
2. Real numbers

Real numbers (R) are of two types:

1. Rational numbers
2. Irrational numbers

Rational numbers (Q)

A number that can be expressed as a/b is known as a rational number where a and b both are integers and b is not zero. Example, 5/7, -5/7, etc.

Properties of rational numbers

• The sum of rational numbers is always a rational number.
• The difference of rational numbers is always a rational number.
• The product of rational numbers is always a rational number.
• When you divide a rational number by a non-zero rational number, it gives you a rational number.

Irrational numbers (Q)

A number that cannot be expressed as a/b is known as an irrational number where a and b both are integers and b is not zero. For example, 'a' is irrational if its exact square root does not exist.

The decimal representation of rational numbers
(i) When you divide a rational number, and there is no remainder, the quotients of such divisions are called terminating decimals.

(ii) When dividing a rational number, if the division does not end, the quotients of such divisions are called non-terminating.

(iii) When a digit or a set of digits repeats continually in a non-terminating decimal, it is known as a recurring decimal.

Surds

If “y” is a positive rational integer and “a” is a positive integer, such that y1/a is irrational, y1/a is called a surd or a radical.

Rationalization 

When a surd is rationalized by multiplying it with its rationalizing factor, it is known as rationalization.