Basics of Numbers for Competitive Exam

#### Digits

Digits are just the single symbols that are used to make numerals.

Examples: Most common numeral systems

__Binary Numeral System__: {0, 1}__Octal Numeral System__: {0, 1, 2, 3, 4, 5, 6, 7}__Decimal Numeral System__: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}__Hexadecimal Numeral System__: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}__Roman Numeral System__: {I, V, X, L, C, D, M}

#### 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

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

Examples:

- 007 is a numeral that represents a number 7.
- Forty is a numeral that represents a number 40.
- VII is a numeral that represents a number 7.

#### Natural Numbers (N)

Counting numbers that are used to count the objects 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

**/**DenominatorExamples:

- 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

**Proper Fraction**: When Numerator is less than Denominator.

Example: 2/3**Improper Fraction**: When Numerator is equal or greater than Denominator.

Example: 2**/**1**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 a Irrational Number.Examples:

- 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)

Basics of Numbers for Competitive Exam

Basics of Numbers for Competitive Exam

Basics of Number Systems for Competitive Exams