Number Types

Number Types Summary

Counting Numbers: Numbers used to count.
Example: - 1,2,3……

Zero: Number to express empty or nothing.
Example:   0

Whole Number: Counting number and zero together.
Example:  0,1,2,3…

Natural Number: Counting Number or Whole Number depending on subject.
Example:  1,2,3…   or 0,1,2,3…

Negative Number: Numbers less than 0 or to count backwards.
Example: … -3,-2,-1. 0 has no sign.

Integer: Negative Number and Whole Number together.
Example: ..-3,-2,-1,0,1,2,3..

Even Number: Any integer that can be divided exactly by 2.
Example: ..-4,-2,0,2,4…

Odd Number: Any integer that cannot be divided exactly by 2.
Example: ..-3,-1,1,3…

Prime Number: An integer greater than 1 that has no positive divisors other than 1 and itself.
Example: 2, 3, 5, 7, 11, 13, 17…

Composite Number: An integer greater than 1 that is not a prime number.
Example: 4,6,8,9,10….

Fraction Number: Part of a whole or Ratio of two integers in a/b form.  a – numerator, b - denominator.
Example: ½, ¼, ¾, 3/8

Proper Fraction Number: In a fraction number, numerator is less than denominator.
Example: 1/3, 2/7

Improper Fraction Number: In a fraction number, numerator is greater than or equal to denominator.
Example: 5/3, 20/10, 11/11

Mixed Fraction Number: Sum of a non-zero integer and a proper fraction.
Example: 2 + 3/4

Rational Number: Any number that can be written as a fraction. p/q : p and q are integers, q is not zero.
Example: -4/3, 3/2, 2..

Irrational Number: A number which cannot be expressed as a ratio of integers.
Example: √1, √2,√3, √5, π, e ..

Real Number: Rational and Irrational Numbers. x : x is a rational or an irrational number.
Example: 2, ¾, √1…

Imaginary Number: A number whose square is a negative Real Number.
Example: √-9 = 3i, -6i, 0.05i, πi... 0 is both real and imaginary.

Complex Number: Combination of a Real Number and an Imaginary Number.  a + bi, where a and b are real, and i is imaginary.
Example: 1+i, 0.5-3i,-2+ πi, √2+i/2..  

Binary Number: Base 2 numeral system.
Example: 0,1

Octal Number: Base 8 numeral system.
Example: 0,1,2,3,4,5,6,7

Decimal Number: Base 10 numeral system. Standard Hindu-Arabic numeral system.
Example: 0,1,2,3,4,5,6,7,8,9

Hexadecimal Number: Base 16 numeral system.
Example: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E

Roman Number: Roman numeral system.
Example: Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ

Scientific Number: A method for writing very small and very large numbers using powers of the base number 10.
Example: 0.000003 = 3.0 e -6 or  3.0 x 10 -6. 234,000,000 = 234 x 10 6

Positive Number: Number greater than 0.
Example: 1,2,3,….

Negative Number: Number less than 0.
Example: …-3,-2,-1

Non Positive Number: Number less than or equal to 0.

Non Negative Number: Number greater than or equal to 0

Algebraic Number: Ay number that is the root  of a non-zero polynomial with rational coefficients

Transcendental Number: Any real or complex number that is not algebraic.
Example: - π, e

Transfinite: Numbers that are greater than any natural number

Cardinal Number: Number that says how many of something in a list.
Example: 1 or 2 or 3…..

Ordinal Number: Number that tells the position of something in a list.
Example: 1st or 2nd or 3rd or 4th or  5th, …

Nominal Number: Number to identify something.
Example: Zip or Postal code, model number

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Related topics:
Indian Numeral   |   Hindu Arabic Numeral   |   Roman Numeral   |   Number System   |   Numeral System

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List of topics: Maths

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Greek Numeral

Greek Numeral or Greek Number:

Greek Numeral or Greek Number are a system of representing numbers using the letters of the Greek alphabet. As the name 'alphabetical' suggests the numerals are based on giving values to the letters of the alphabet. There are 27 letters in the Greek alphabet in which 3 letters (digamma, koppa, and san) are obsolete ones. So there are 24 letters in classical Greek alphabet.

Classical Greek Alphabet:

Name	Upper case	Lowercase
Alpha	Α	α
Beta	Β	β
Gamma	Γ	γ
Delta	Δ	δ
Epsilon	Ε	ε
Digamma	Obsolete	Obsolete
Zeta	Ζ	ζ
Eta	Η	η
Theta	Θ	θ
Iota	Ι	ι
Kappa	Κ	κ
Lambda	Λ	λ
Mu	Μ	μ
Nu	Ν	ν
Xi or ksi	Ξ	ξ
Omicron	Ο	ο
Pi	Π	π
Koppa	Obsolete	Obsolete
Rho	Ρ	ρ
Sigma	Σ	σ
Tau	Τ	τ
Upsilon	Υ	υ
Phi	Φ	φ
Chi	Χ	χ
Psi	Ψ	ψ
Omega	Ω	ω
San or sampi	Obsolete	Obsolete

The first nine of these letters were taken as the symbols for 1, 2, ... , 9.

Symbol	Value
α	1
β	2
γ	3
δ	4
ε	5
ϛ	6
ζ	7
η	8
θ	9

The next nine letters were taken as the symbols for 10, 20, ... , 90.

Symbol	Value
ι	10
κ	20
λ	30
μ	40
ν	50
ξ	60
ο	70
π	80
ϟ	90

The remaining nine letters were taken as the symbols for 100, 200, ... , 900.

Symbol	Value
ρ	100
σ	200
τ	300
υ	400
φ	500
χ	600
ψ	700
ω	800
ϡ	900

Numbers were formed by the additive principle. For example 21, 22, ... , 29 were written:

Symbol	Value
κα	21
κβ	22
κγ	23
κδ	24
κε	25
κϛ	26
κζ	27
κη	28
κθ	29

Numbers 221,222, ... , 229 were written:

Symbol	Value
σκα	221
σκβ	222
σκγ	223
σκδ	224
σκε	225
σκϛ	226
σκζ	227
σκη	28
σκθ	229

Alphabetic Greek Numerals:

	Units	Tens	Hundreds
1	α	ι	ρ
2	β	κ	σ
3	γ	λ	τ
4	δ	μ	υ
5	ε	ν	φ
6	ϛ	ξ	χ
7	ζ	ο	ψ
8	η	π	ω
9	θ	ϟ	ϡ

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Indian Numeral   |   Hindu Arabic Numeral   |   Roman Numeral   |   Number System   |   Numeral System

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Indian Numeral

Indian Numerals or Indian Numbers are symbols representing numbers in India. There are different languages in India and each is having its own numerals.

Indian Numerals based on Devanagari script:

Modern Devanagari	० १ २ ३ ४ ५ ६ ७ ८ ९
Bengali – Assamese	০ ১ ২ ৩ ৪ ৫ ৬ ৭ ৮ ৯
Gujarati	૦ ૧ ૨ ૩ ૪ ૫ ૬ ૭ ૮ ૯
Gurmukhi – Punjabi	੦ ੧ ੨ ੩ ੪ ੫ ੬ ੭ ੮ ੯
Odia	୦ ୧ ୨ ୩ ୪ ୫ ୬ ୭ ୮ ୯

South Indian Languages:

Tamil	൦ ௧ ௨ ௩ ௪ ௫ ௬ ௭ ௮ ௯
Malayalam	൦ ൧ ൨ ൩ ൪ ൫ ൬ ൭ ൮ ൯
Telugu	౦ ౧ ౨ ౩ ౪ ౫ ౬ ౭ ౮ ౯
Kannada	೦ ೧ ೨ ೩ ೪ ೫ ೬ ೭ ೮ ೯

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Greek Numeral   |   Hindu Arabic Numeral   |   Roman Numeral   |   Number System   |   Numeral System

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Hindu Arabic Numeral

Hindu-Arabic Numeral Figure & Symbol:

Hindu-Arabic numeral system or Hindu-Arabic number system is a decimal place-value numeral system. This is the numeral system that we are using today. This system has
nine figures 1, 2, 3, 4, 5, 6, 7, 8, 9 and a symbol 0
in it. With the figures and symbol, any number can be represented easily. The Hindu-Arabic Numerals requires a zero to handle the empty powers of ten as in 105, 205, and 305.

The Hindu-Arabic Numerals is originated in India and transmitted to the West via the Arabs. In ancient India, there were number symbols to represent 1 through 9 and also to represent 10 through 90. Later the Indians evidently dropped the symbols for numbers higher than 9 and began to use their symbols for 1 through 9.

An Italian mathematician, Leonardo Pisano Bogollo, (1170-1250) also known as Leonardo of Pisa or simply Fibonacci is best known to the modern world for the spreading of the Hindu-Arabic numeral system in Europe.

European called this as Arabic Numerals since they learned from Arabs. Arabs refer to their numerals as Indian Numerals. In academic circles they are called the Hindu-Arabic or Indo-Arabic Numerals. 

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Roman Numeral

Roman Numerals or Roman Numbers are originated in ancient Rome. Its letters are derived from earlier non alphabetical symbols. Roman numerals are combination of seven letters in the table below.

Roman Numerals: Letters and its Value

Letter	Value
I or i	1
V or v	5
X or x	10
L or l	50
C or c	100
D or d	500
M or m	1000

There is no Zero in Roman Numerals. If smaller numbers follow larger numbers, the numbers are added. If a smaller number precedes a larger number, the smaller number is subtracted from the larger.
Based on the above table and rule, the first ten roman numerals are defined in the table below.

Numeral		Value
I	1	1
II	1+1	2
III	1+1+1	3
IV	5-1	4
V	5	5
VI	5+1	6
VII	5+1+1	7
VIII	5+1+1+1	8
IX	10-1	9
X	10	10

Examples of Roman Numerals and its value.

Numeral		Value
XV	10+5	15
XX	10+10	20
MD	1000+500	1500
XD	500-10	490
XM	1000-10	900
MCMLXXXIV	1000+(1000-100)+50+10+10+10+(5-1)	1984

Fractions:

Fraction	Roman Numeral
1/12	.
2/12	..
3/12	…
4/12	….
5/12	…..
6/12	S
7/12	S.
8/12	S..
9/12	S…
10/12	S….
11/12	S…..
12/12	I

Large Numbers:

Roman Numeral	Value
|Ɔ	500
C|Ɔ	1000
|ƆƆ	5000
CC|ƆƆ	10000
|ƆƆƆ	50000
CCC|ƆƆƆ	100000

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Number System

A number is a mathematical object used to count, measure and label. Numbers can be classified into sets called Number Systems.

Main Number System:

N	Natural	0, 1, 2, 3, 4, ... or 1, 2, 3, 4, ...
Z	Integer	..., −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, ...
Q	Rational	a/b where a and b are integers and b is not 0
R	Real	The limit of a convergent sequence of rational numbers
C	Complex	a + bi where a and b are real numbers and i is the square root of −1

Each of the number systems mentioned above is a proper subset of the next number system. Symbolically, N ⊂ Z ⊂ Q ⊂ R ⊂ C.

Summary:

Counting Numbers: Numbers to count.
Example: 1,2,3…… 

Zero: Number to express empty or nothing.
Example: 0

Whole Number: Counting number with zero.
Example: 0,1,2,3…..

Natural Number: Counting Number or Whole Number depending on subject

Negative Number: Numbers to count backwards.
Example: … -3,-2,-1

Integer: Negative Number with Whole Number.
Example: ..-3,-2,-1,0,1,2,3..

Even Number: Any integer that can be divided exactly by 2.
Example: ..-4,-2,0,2,4…

Odd Number: Any integer that cannot be divided exactly by 2.
Example: ..-3,-1,1,3…

Prime Number: An integer greater than 1 that has no positive divisors other than 1 and itself.
Example: 2, 3, 5, 7, 11, 13, 17…

Composite Number: An integer greater than 1 that is not a prime number.
Example: 4,6,8,9,10….

Fraction: Part of a whole.
Example: ½, ¼, ¾, 3/8…

Rational Number: Any number that can be written as a fraction. p/q : p and q are integers, q is not zero. Example: -4/3, 3/2, 2..

Irrational Number:  A number which cannot be expressed as a ratio of integers.
Example: √1, √2,√3, √5, π, e ..

Real Number: Rational and Irrational Numbers. x : x is a rational or an irrational number.
Example: 2, ¾, √1…

Imaginary Number: A number whose square is a negative Real Number.
Example: √-9 = 3i, -6i, 0.05i, πi..

Complex Number: Combination of a Real Number and an Imaginary Number.  a + bi, where a and b are real, and i is imaginary.
Example: 1+i, 0.5-3i,-2+ πi, √2+i/2.. 

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Numeral System

What is Numeral System?

Numerals are the symbols used to represent numbers. A notational symbol that represents a number is called a numeral.

A numeral system is a writing system for expressing numbers.  A mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

Numeral System List:
By Culture:

Indian	Chinese	Roman	Greek	Hindu Arabic
0	零	Ⅰ	α	0
१	一	Ⅱ	β	1
२	二	Ⅲ	γ	2
३	三	Ⅳ	δ	3
४	四	Ⅴ	ε	4
५	五	Ⅵ	ϝ	5
६	六	Ⅶ	ζ	6
७	七	Ⅷ	η	7
८	八	Ⅸ	θ	8
९	九	Ⅹ	ι	9

By Positional Notation:

Name	Base
Unary	1
Binary	2
Ternary	3
Quaternary	4
Quinary	5
Senary	6
Octal	8
Decimal	10
Undecimal	11
Duodecimal	12
Tridecimal	13
Tertadecimal	14
Pentadecimal	15
Hexadecimal	16
Vigesimal	20
Tetravigesimal	24
Heptavigesimal	27
Trigesimal	30
Duotrigesimal	32
Hexatrigesimal	36
Sexagesimal	60
Tetrasexagesimal	64
Pentoctogesimal	85
Negabinary	-2
Negaternary	-3
Negadecimal	-10
Quarter Imaginary	2i
Twindragon	−1 ± i
Golden ratio base	φ
Base exponential	e
Base "Pi-nary"	π
Base square root of 2	√2
Base twelfth root of 2	¹²√2

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