STD VIII – NUMBER SYSTEM (Hybrid)

RATIONAL NUMBERS

Numbers that can be expressed in the form pq, where p and q are integers and q ≠ 0, are known as rational numbers. The collection of rational numbers is denoted by Q.

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are integers

Properties of rational Numbers

Closure

Commutativity (a+b=b+a) and (a x b = b x a) |

Associativity  a×(b×c)=(a×b)×c and a+(b+c)=(a+b)+c

Number Line

Every point in a number line, represents a number

Between any 2 rational numbers there exists infinitely many rational numbers

Exponents

Very large numbers, for example, 1685742300000 are difficult to read, understand and compare.

Exponents are shorthand for repeated multiplication of the same thing by itself, and it’s power refers to the number of times it is multiplied.

Squares and Square Roots

In mathematics, students learn about numbers and different operations on them.

A square of an integer is the product of some integer with itself. Similarly, the square root of a number is an integer which when multiplied by itself give this number. In this topic, we will increase our understanding of squares, square roots, and will learn about ways of finding them.

Cubes and Cube Roots

In arithmetic and algebra, the cube of a number n is its third power, the result of the number multiplied by itself twice:

n3 = n × n × n.

It is also the number multiplied by its square:

n3 = n × n2.

Playing with Numbers

Calculations with numbers are done with arithmetical operations, the most familiar being the addition, subtraction, multiplication, division, and exponentiation.

Their study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of numbers.

Sets

In mathematics, a set is a well-defined collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}