# Basic Mathematics – Numbers

#### 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 (adsbygoogle = window.adsbygoogle || []).push({}); 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/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 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.

####   Representation 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)