Basics of Numbers for Competitive Exam

#### Basics of Numbers for Competitive Exam

##### What are Digits?

Digits are just the single symbols that are used to make numerals.
Examples: Most common numeral systems
(1) Binary Numeral System: {0, 1}
(2) Octal Numeral System: {0, 1, 2, 3, 4, 5, 6, 7}
(3) Decimal Numeral System: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
(4) Hexadecimal Numeral System: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}
(5) Roman Numeral System: {I, V, X, L, C, D, M}

##### What are Numerals?

Single-digit or combinations of digits are called numerals. Letters or figures can also be numerals.
Examples:
007 is a numeral and it is made of three digits i.e 0, 0, 7.
Forty is also a numeral.
VII is numeral.

##### Numbers

A numeral is a name or representation given to a Numbers when they are used to indicate the magnitude of any quantity.

Examples:
007 is a numeral that represents the number 7.
Forty is a numeral that represents the number 40.
VII is a numeral that represents the number 7.

##### Natural Numbers (N)

Counting numbers that are used to count the objects are called Natural Numbers. All positive non-zero numbers are natural numbers.
{1, 2, 3, and so on}

##### Whole Numbers (W)

All the natural numbers and 0 are together are called Whole Numbers.
{0, 1, 2, 3, and so on} Or {0, N}

##### Integers (I)

All the whole numbers along with their negatives called Integers.
{0, +1, -1, +2, -2, +3, -3, and so on} Or {0, N, -N}

##### Various other combinations of integers:

Positive integers: {1, 2, 3, and so on}
Negative integers: {-1, -2, -3, and so on}
Non Negative integers: {0, 1, 2, 3, and so on}
Non Positive integers: {0, -1, -2, -3, and so on}
Non Zero integers: {1, -1, 2, -2, 3, -3, and so on}

##### Fractions

A part of a whole number is called fraction or fraction number.
Representation of a Fraction = Numerator/Denominator

Examples:
3 parts of 7 i.e 3 out of 7 is a fraction, represented by 3/7.
1 part of 2 i.e 1 out of 2 is a fraction, represented by 1/2.

#### Types of fractions

(1) Proper Fraction: When Numerator is less than Denominator.
Example: 2/3

(2) Improper Fraction: When Numerator is equal or greater than Denominator.
Example: 2/1

(3) Mixed Fraction: A combination of a proper fraction and a whole number is called a mixed fraction.
Example: 3+1/2

#### Rational Numbers (Q)

Any number that can be expressed as a fraction or a quotient (p/q form) is called a Rational Number where (q ≠ 0) and (p & q) both are co-prime numbers i.e (p & q) don’t have any common factor.

Examples:
3 = 3/1
-5 = -5/1
2/3
0.87 = 87/100

#### Irrational Numbers

Any number that can not be expressed as a fraction or a quotient (p/q form) is called an Irrational Number.
Examples:
The square root of 2.
e
π

#### Real Numbers (R)

All the rational and irrational numbers together are called Real Numbers. All the natural numbers, whole numbers, fractions, etc are part of real numbers.

Imaginary Numbers (i) Any number whose square is negative, is called an Imaginary Number. Squares of all the real numbers are always positive.   Examples:
i
3i
19i
Where square of i = -1 i.e (i x i = -1)

#### Complex Numbers (C)

Combination (Addition or subtraction) of real and imaginary numbers. [C = R ± i]
Examples:
3 + 2i
7 – 6i

Where square of i = -1 i.e (i x i = -1)

Click here for more Topics on Mathematics