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Maths:- Number Notation

Number Notation

(Math | General | Number Notation)

Names | SI (Metric) Prefixes | Roman Numerals | Bases

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

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

Some people use a comma to mark every 3 digits. It just keeps track of the digits and makes the numbers easier to read.

Beyond a million, the names of the numbers differ depending where you live. The places are grouped by thousands in America and France, by the millions in Great Britain and Germany.

Name	American-French	English-German
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
googolplex	1 with a googol of zeros

FractionsDigits to the right of the decimal point represent the fractional part of the decimal number. Each place value has a value that is one tenth the value to the immediate left of it.

Number	Name	Fraction
.1	tenth	1/10
.01	hundredth	1/100
.001	thousandth	1/1000
.0001	ten thousandth	1/10000
.00001	hundred thousandth	1/100000

Examples:

0.234 = 234/1000 (said - point 2 3 4, or 234 thousandths, or two hundred thirty four thousandths)

4.83 = 4 83/100 (said - 4 point 8 3, or 4 and 83 hundredths)

SI Prefixes

Number Prefix Symbol 10 1 deka- da 10 2 hecto- h 10 3 kilo- k 10 6 mega- M 10 9 giga- G 10 12 tera- T 10 15 peta- P 10 18 exa- E 10 21 zeta- Z 10 24 yotta- Y

Number Prefix Symbol 10 -1 deci- d 10 -2 centi- c 10 -3 milli- m 10 -6 micro- u (greek mu) 10 -9 nano- n 10 -12 pico- p 10 -15 femto- f 10 -18 atto- a 10 -21 zepto- z 10 -24 yocto- y

Roman Numerals

I=1		(I with a bar is not used)
V=5		_ V=5,000
X=10		_ X=10,000
L=50		_ L=50,000
C=100		_ C = 100 000
D=500		_ D=500,000
M=1,000		_ M=1,000,000

Roman Numeral Calculator

Examples:

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

There is no zero in the roman numeral system.

The numbers are built starting from the largest number on the left, and adding smaller numbers to the right. All the numerals are then added together.

The exception is the subtracted numerals, if a numeral is before a larger numeral, you subtract the first numeral from the second. That is, IX is 10 - 1= 9.

This only works for one small numeral before one larger numeral - for example, IIX is not 8, it is not a recognized roman numeral.

There is no place value in this system - the number III is 3, not 111.

Number Base Systems

Decimal(10)	Binary(2)	Ternary(3)	Octal(8)	Hexadecimal(16)
0	0	0	0	0
1	1	1	1	1
2	10	2	2	2
3	11	10	3	3
4	100	11	4	4
5	101	12	5	5
6	110	20	6	6
7	111	21	7	7
8	1000	22	10	8
9	1001	100	11	9
10	1010	101	12	A
11	1011	102	13	B
12	1100	110	14	C
13	1101	111	15	D
14	1110	112	16	E
15	1111	120	17	F
16	10000	121	20	10
17	10001	122	21	11
18	10010	200	22	12
19	10011	201	23	13
20	10100	202	24	14

Each digit can only count up to the value of one less than the base. In hexadecimal, the letters A - F are used to represent the digits 10 - 15, so they would only use one character.