Number Notation

Number Notation

Number notation refers to the different ways in which numbers can be represented or written. Depending on the context and the mathematical or cultural conventions being used, numbers can be expressed in various notations. Here are some common types of number notation:

Standard Notation:

This is the most common way of writing numbers using digits (0-9). It follows the place value system, where each digit’s position represents a power of 10.

For example, the number 2,345 is written in standard notation as 2345.

Scientific Notation:

This notation is used to express very large or very small numbers in a more compact form. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10.

For example, the speed of light, 299,792,458 meters per second, can be written in scientific notation as 2.99792458 × 10^8 m/s.

Engineering Notation:

Similar to scientific notation, engineering notation is used primarily in engineering and physical sciences. It also uses powers of 10, but the exponent is always a multiple of 3.

For example, the speed of light in engineering notation might be written as 299.792 × 10^6 m/s.

Fraction Notation:

Numbers can be expressed as fractions, where a numerator is divided by a denominator.

For example, 3/4 represents the fraction three-quarters.

Roman Numerals:

This ancient notation system uses letters of the Roman alphabet (I, V, X, L, C, D, M) to represent numbers. It was commonly used in ancient Rome and is still sometimes used today for certain purposes, such as numbering chapters or sections.

Binary Notation:

Computers use a binary number system, which consists of only two digits: 0 and 1. Binary notation is used to represent data and perform calculations in computer systems.

Hexadecimal Notation:

Another base used in computing is hexadecimal, which uses digits 0-9 and letters A-F to represent values. It’s often used to represent memory addresses and data in computer programming.

Octal Notation:

Octal is base-8 notation, which uses digits 0-7. It’s less common than binary or hexadecimal but can still be encountered in some computing contexts.

Place Value Notation:

This is a more general term referring to any system where the value of a digit is determined by its position within a number. It includes standard notation and other positional numeral systems.

Mixed Notation:

In some cases, a combination of different notations might be used.

For example, a number might be expressed using a mix of standard notation and scientific notation.

The choice of notation depends on the application and the level of precision or clarity required. Different fields of science, mathematics, and technology may prefer specific notations based on their requirements and conventions.

 

Hierarchy Of Decimal Numbers

Number	Name	How Many
0	Zero
1	One
2	Two
3	Three
4	Four
5	Five
6	Six
7	Seven
8	Eight
9	Nine
10	Ten
20	Twenty	Two Tens
30	Thirty	Three Tens
40	Forty	Four Tens
50	Fifty	Five Tens
60	Sixty	Six Tens
70	Seventy	Seven Tens
80	Eighty	Eight Tens
90	Ninety	Nine Tens
100	One Hundred	Ten Tens
200	Two Hundred	Twenty Tens
300	Three Hundred	Thirty Tens
400	Four Hundred	Forty Tens
500	Five Hundred	Fifty Tens
600	Six Hundred	Sixty Tens
700	Seven Hundred	Seventy Tens
800	Eight Hundred	Eighty Tens
900	Nine Hundred	Ninety Tens

 

Number	Name	How Many
100	one hundred	ten tens
1,000	one thousand	ten hundreds
10,000	ten thousand	ten thousands
100,000	one hundred thousand	one hundred thousands
1,000,000	one million	one thousand thousands

 

 

Name	Short Scale (Value)	Long Scale (Value)
million	1,000,000	1,000,000
billion	1,000,000,000 (a thousand millions)	1,000,000,000,000 (a million millions)
trillion	1 with 12 zeros	1 with 18 zeros
quadrillion	1 with 15 zeros	1 with 24 zeros
quintillion	1 with 18 zeros	1 with 30 zeros
sextillion	1 with 21 zeros	1 with 36 zeros
septillion	1 with 24 zeros	1 with 42 zeros
octillion	1 with 27 zeros	1 with 48 zeros
googol	1 with 100 zeros	1 with 100 zeros
googolplex	1 with a googol of zeros	1 with a googol of zeros

 

Fractions

Digits to the Right of the decimal point represent the fractional part of the decimal number. 

Number	Name	Fraction
0.1	tenth	1/10
0.01	hundredth	1/100
0.001	thousandth	1/1000
0.0001	ten thousandth	1/10000
0.00001	hundred thousandth	1/100000

 

SI (Metric) Prefixes 

 

Prefix	Symbol	Power of 10
Yotta	Y	10^24
Zetta	Z	10^21
Exa	E	10^18
Peta	P	10^15
Tera	T	10^12
Giga	G	10^9
Mega	M	10^6
Kilo	k	10^3
Hecto	h	10^2
Deca	da	10^1
(Base)		10^0
Deci	d	10^-1
Centi	c	10^-2
Milli	m	10^-3
Micro	μ	10^-6
Nano	n	10^-9
Pico	p	10^-12
Femto	f	10^-15
Atto	a	10^-18
Zepto	z	10^-21
Yocto	y	10^-24

 

Roman Numerals

 

Roman Numeral	Value	Large Value Variation
I	1
V	5	5,000
X	10	10,000
L	50	50,000
C	100	100,000
D	500	500,000
M	1,000	1,000,000

Please note that the “large value variations” (e.g., V=5,000, X=10,000, etc.) are not standard or widely recognized in Roman numeral notation. Roman numerals are typically used for relatively smaller numbers, and for larger numbers, other numeral systems are more practical.

There is no zero in the roman numeral system.

Number	Roman Numeral
1	I
2	II
3	III
4	IV
5	V
6	VI
7	VII
8	VIII
9	IX
10	X
11	XI
12	XII
13	XIII
14	XIV
15	XV
16	XVI
17	XVII
18	XVIII
19	XIX
20	XX
21	XXI
25	XXV
30	XXX
40	XL
49	XLIX
50	L
51	LI
60	LX
70	LXX
80	LXXX
90	XC
99	XCIX

Please note that Roman numerals are a numeral system used in ancient Rome and have been used historically for various purposes. They are not commonly used for arithmetic calculations in modern times.

 

Overview of various number base systems, including their base value, representation, and some examples:

Base	Name	Digits	Examples (decimal)
2	Binary	0, 1	10101 (21)
3	Ternary	0, 1, 2	201 (19)
4	Quaternary	0, 1, 2, 3	123 (27)
5	Quinary	0, 1, 2, 3, 4	234 (44)
6	Senary	0, 1, 2, 3, 4, 5	405 (215)
7	Septenary	0, 1, 2, 3, 4, 5, 6	623 (331)
8	Octal	0, 1, 2, 3, 4, 5, 6, 7	37 (31)
9	Nonary	0, 1, 2, 3, 4, 5, 6, 7, 8	86 (77)
10	Decimal	0, 1, 2, …, 9	123 (123)
11	Undecimal	0, 1, 2, …, A (10)	A3 (124)
12	Duodecimal	0, 1, 2, …, B (11)	B5 (141)
16	Hexadecimal	0, 1, 2, …, 9, A, …, F (15)	1A7 (423)
20	Vigesimal	0, 1, 2, …, J (19)	1J9 (419)
60	Sexagesimal	0, 1, 2, …, 9, A, …, Z, a, …, z	1z (60)

In this table, “decimal” refers to the base-10 numbering system, which is the standard system we use in everyday life. Other bases are used in various applications, such as computer science, mathematics, and different cultures. Each digit in a number represents a certain value based on the base of the number system.

Number Base Systems

Decimal (10)	Binary (2)	Ternary (3)	Octal (8)	Hexadecimal (16)
0	0000	00	00	00
1	0001	01	01	01
2	0010	02	02	02
3	0011	10	03	03
4	0100	11	04	04
5	0101	12	05	05
6	0110	20	06	06
7	0111	21	07	07
8	1000	22	10	08
9	1001	100	11	09
10	1010	101	12	0A
11	1011	102	13	0B
12	1100	110	14	0C
13	1101	111	15	0D
14	1110	112	16	0E
15	1111	120	17	0F

Please note that for the base systems with digits greater than 9 (i.e., hexadecimal), letters are used to represent values greater than 9 (A = 10, B = 11, C = 12, etc.).

 

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