Numbers are classified as natural numbers, whole numbers, integers, rational numbers and irrational numbers. Rational and Irrational numbers together constitute the system of real numbers.
Natural Numbers (N): Counting numbers 1, 2, 3, 4, and so on. Smallest natural number is 1.
Whole Numbers (W): Natural numbers including 0. Smallest whole number is 0.
Integers (I): Whole numbers including negatives of natural numbers. Integers are ..., -3, -2, -1, 0, 1, 2, 3, ... .
Rational Number (Q): Number p/q is a rational number if p and q are integers and q ≠ 0.
Standard form of a rational number: p/q is said to be in standard form if q is positive and p and q are co-primes.
Every integer is a rational number but every rational number is not an integer. Every fraction is a rational number but vice-versa is not always true.
Equivalent form of a rational number: Two rational numbers p/q and r/s are said to be equivalent if ps = rq.
Rational numbers on number line: Every rational number can be represented on a number line. Corresponding to each rational number, there exists a unique point on the number line but converse is not always true.
Comparison of rational numbers: Reduce the numbers with the same denominator and compare their numerators. On a number line the greater rational number lies to the right of the smaller.
Decimal representation of rational numbers: Process of expressing a rational number into decimal form is to carry out the process of long division using decimal.
Rational number is either a terminating decimal or a non-terminating repeating decimal.
Rational numbers between two rational numbers: There exists infinitely many rational numbers between two rational numbers. A rational number between two rational numbers can be found by calculating the average of given numbers.
Irrational numbers: A decimal expression which is neither terminating nor repeating represents an irrational number. Numbers other than rational numbers like √2, √3 are examples of irrational numbers.
Real Numbers: Rational and Irrational numbers together constitute the system of real numbers.