Number Systems

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Theory

‘Number System’ is an important topic for SSC exams. It is the basic topic in Quantitative Aptitude where the introduction of numbers and their applications are given. In this VBODMAS rule will also be covered where the calculation can be done when different brackets are available.

Natural Number - These are the counting numbers from 1 to infinite(∞).

Whole Number - If in the natural numbers, 0 is also included then it becomes the whole number. These are from 0 to infinite(∞).

Integers - If in the whole number negative numbers are included then it becomes the Integers.

Rational Number - A number which can be expressed in the form of $$\frac{P}{Q}$$ are called Rational numbers. For example $$\frac{9}{11}$$.

Irrational Number - A number that cannot be expressed in the form of $$\frac{P}{Q}$$ are called Irrational numbers. For example $$\sqrt{7}$$.

Real Numbers - If we combine Rational and Irrational numbers, then it will become Real numbers.

Imaginary Numbers - A number that can be represented in form of (i) or not exist in the reality are called Imaginary numbers.

Complex Numbers - These are the combination of real and imaginary numbers. For example (11+13i).

Prime Numbers - Those numbers which are divisible by 1 and itself are called Prime numbers. Only 2 is an even number which is prime and others prime numbers are odd. For example 2, 3, 5, 7 and 11 etc..

Composite Numbers - Those numbers which are not prime are called Composite numbers.

VBODMAS -

V - Vinculum

B - Bracket (), {}, []

Here small bracket, then curly bracket and in the last big bracket will be solved.

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction

The above given things will be solved in respective manner while solving a simplification question.

Formula

Sum of the first n natural numbers = $$n\times\frac{(n+1)}{2}$$

Sum of the first n odd numbers = $$n^{2}$$

Sum of the first n even numbers = n(n+1)

Sum of the square of first n natural numbers = $$\frac{n(n+1)(2n+1)}{6}$$

Sum of the cube of first n natural numbers = $$[n\times\frac{(n+1)}{2}]^{2}$$

Solved Example

Q) Find out the sum of the first 11 odd numbers.

Sol.

Sum of the first 11 odd numbers = $$n^{2}$$ = $$11^{2}$$

= 121

Solved Example

Q) Find out the value of $$68[39\times(8-3)\div13+6-4]$$

Sol.

= $$68[39\times(8-3)\div13+6-4]$$

= $$68[39\times5\div13+6-4]$$

= $$68[15+6-4]$$

= $$68\times17$$

= 1156

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