Revision: Numbers Mathematics SSLC (English Medium) Class 8 Tamil Nadu Board of Secondary Education

Natural numbers are the numbers used for counting, beginning from 1 onwards.
They are denoted by the set N = {1, 2, 3, 4, 5, …}

Whole numbers are a foundational concept in mathematics, encompassing all non-negative integers starting from zero.
Example: 0, 1, 2, 3, 4, ..., 367, 368, ..., 237105, ...

The numbers −1, −2, −3, … (to the left of zero) are negative numbers or negative integers, and the numbers 1, 2, 3, … (to the right of zero) are positive numbers or positive integers.
Hence, the new set of numbers …, −3, −2, −1, 0, 1, 2, 3,… are called integers.

A number that can be expressed in the form `p/q`, where p and q are integers, and q is not equal to zero "q ≠ 0", is called a rational number. The numbers `-2/7, 3/8, 3` etc., are rational numbers.

Positive Rational Number: When the numerator and denominator, both, are positive integers, it is a positive rational number. `3/8, 5/7, 2/9` etc. are positive rational numbers.

Negative rational numbers: When either the numerator or the denominator is a negative integer, it is a negative rational number. `-5/7, -3/8, -9/5` etc. are negative rational numbers.

Square numbers: A number which produces a specified number when multiplied by itself are known as square numbers.

Cube numbers: Numbers obtained when a number is multiplied by itself three times are known as cube numbers.

Exponents: An exponent is a numerical notation that indicates the number of times a number is to be multiplied by itself. Exponent is also called as power or index. Example, 7⁵.

a° = 1.

a¹ = a.

a^{- m} = `1/a^m`

For any non-zero integer a, where m and n are whole numbers, a^m × aⁿ =a^{m + n}.

For any non-zero integer a, where m and n are whole numbers and m > n, a^m ÷ aⁿ = a^{m – n}.

If a is a non-zero rational number and m and n are integers, then (a^m)ⁿ = a^{m × n} = a^mn.

For any non-zero integer a, where m is any whole number, a^m × b^m = (ab)^m.

a^m ÷ b^m = `a^m/b^m = (a/b)^m`, where a, and b are any non-zero integers and m is a whole number.