1. Here is an interesting and lovely way to look at the beauty of mathematics, and of God, the sum of all wonders. The Beauty of Mathematics Wonderful World
2. 1 x 8 + 1 = 9 12 x 8 + 2 = 9 8 123 x 8 + 3 = 9 8 7 1234 x 8 + 4 = 9 8 7 6 12345 x 8 + 5 = 9 8 7 6 5 123456 x 8 + 6 = 9 8 7 6 5 4 1234567 x 8 + 7 = 9 8 7 6 5 4 3 12345678 x 8 + 8 = 9 8 7 6 5 4 3 2 123456789 x 8 + 9 = 9 8 7 6 5 4 3 2 1
3. 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 123456 x 9 + 7 = 1111111 1234567 x 9 + 8 = 11111111 12345678 x 9 + 9 = 111111111 123456789 x 9 +10= 1111111111
4. 9 x 9 + 7 = 88 98 x 9 + 6 = 888 987 x 9 + 5 = 8888 9876 x 9 + 4 = 88888 98765 x 9 + 3 = 888888 987654 x 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888 Brilliant, isn’t it?
5. 1 x 1 = 1 11 x 11 = 1 2 1 111 x 111 = 1 2 3 2 1 1111 x 1111 = 1 2 3 4 3 2 1 11111 x 11111 = 1 2 3 4 5 4 3 2 1 111111 x 111111 = 1 2 3 4 5 6 5 4 3 2 1 1111111 x 1111111 = 1 2 3 4 5 6 7 6 5 4 3 2 1 11111111 x 11111111 = 123456787654321 111111111 x 111111111 = 12345678987654321 And look at this symmetry:
6. 101% From a strictly mathematical viewpoint: What Equals 100%? What does it mean to give MORE than 100%? Ever wonder about those people who say they are giving more than 100%? We have all been in situations where someone wants you to GIVE OVER 100% How about ACHIEVING 101%? What equals 100% in life? Now, take a look at this…
7. Here’s a little mathematical formula that might help Answer these questions:
8. If: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Is represented as: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26.
9. If: H-A-R-D-W-O-R- K 8+1+18+4+23+15+18+11 = 98% And: K-N-O-W-L-E-D-G-E 11+14+15+23+12+5+4+7+5 = 96%
10. But: A-T-T-I-T-U-D-E 1+20+20+9+20+21+4+5 = 100% THEN , look how far the love of God will take you: L-O-V-E-O-F-G-O-D 12+15+22+5+15+6+7+15+4 = 101%
11. Therefore, one can conclude with mathematical certainty that: While Hard Work and Knowledge will get you close, and Attitude will Get you there , It’s the Love of God that will put you over the top!
12. Have a great day… and that God bless you! Diramar setembro,2008 www.slideshare.net/Diramar www.pdmfedc.multiply.com (Internet search)
+ Diramar ***Diramar ***, 2 years ago
Sunday, November 8, 2009
beauty of math2
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
And finally, take a look at this symmetry:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321
Brilliant, isn't it?
TOP
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
And finally, take a look at this symmetry:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321
Brilliant, isn't it?
TOP
beauty of math
Many mathematicians derive aesthetic pleasure from their work, and from mathematics in general. They express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful. Sometimes mathematicians describe mathematics as an art form or, at a minimum, as a creative activity. Comparisons are often made with music and poetry. Bertrand Russell expressed his sense of mathematical beauty in these words:
Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.[1]
Paul Erdős expressed his views on the ineffability of mathematics when he said, "Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is."[2]
famous problem
Godelphoto.gif
Kurt Gödel's Incompleteness Theorem A summary of the revolution that this great logician brought to the foundation of mathematics - see also Russell's paradox
Fermat.jpg
Fermat's Last Theorem Facts and pointers for this famous problem that remained unsolved for more than 350 years and the final milestones to the proof
infinity.gif
Cantor's Continuum Hypothesis The different faces of infinity
The Most Beautiful Formula Euler's almost magic formula that relates five fundamental numbers: e, i, Pi, 0 and 1 (and a corollary: i raised to itself is real)
The Most Famous Open Question Riemann Hypothesis: the most sought-after accomplishment in number theory
medal.gif
Famous Problems in Mathematics A page maintained by Alex Lopez-Ortiz. Topics include the famous Four Colour Theorem, the 23 Hilbert Problems that guided research in the 20th century and some famous unsolved problems, including Goldbach's and Twin Primes conjectures
1,2,3,5,7,11,...
The Prime Number Theorem The article from Encyclopædia Britannica on this astonishing property of the infinite population of prime numbers
4color.jpg
The Four Color Theorem History, a summary of a new proof and a four-coloring algorithm found. By Neil Robertson, Daniel Sanders, Paul Seymour and Robin Thomas
Kurt Gödel's Incompleteness Theorem A summary of the revolution that this great logician brought to the foundation of mathematics - see also Russell's paradox
Fermat.jpg
Fermat's Last Theorem Facts and pointers for this famous problem that remained unsolved for more than 350 years and the final milestones to the proof
infinity.gif
Cantor's Continuum Hypothesis The different faces of infinity
The Most Beautiful Formula Euler's almost magic formula that relates five fundamental numbers: e, i, Pi, 0 and 1 (and a corollary: i raised to itself is real)
The Most Famous Open Question Riemann Hypothesis: the most sought-after accomplishment in number theory
medal.gif
Famous Problems in Mathematics A page maintained by Alex Lopez-Ortiz. Topics include the famous Four Colour Theorem, the 23 Hilbert Problems that guided research in the 20th century and some famous unsolved problems, including Goldbach's and Twin Primes conjectures
1,2,3,5,7,11,...
The Prime Number Theorem The article from Encyclopædia Britannica on this astonishing property of the infinite population of prime numbers
4color.jpg
The Four Color Theorem History, a summary of a new proof and a four-coloring algorithm found. By Neil Robertson, Daniel Sanders, Paul Seymour and Robin Thomas
space
The study of space originates with geometry – in particular, Euclidean geometry. Trigonometry is the branch of mathematics that deals with relationships between the sides and the angles of triangles and with the trigonometric functions; it combines space and numbers, and encompasses the well-known Pythagorean theorem. The modern study of space generalizes these ideas to include higher-dimensional geometry, non-Euclidean geometries (which play a central role in general relativity) and topology. Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry. Within differential geometry are the concepts of fiber bundles and calculus on manifolds, in particular, vector and tensor calculus. Within algebraic geometry is the description of geometric objects as solution sets of polynomial equations, combining the concepts of quantity and space, and also the study of topological groups, which combine structure and space. Lie groups are used to study space, structure, and change. Topology in all its many ramifications may have been the greatest growth area in 20th century mathematics; it includes point-set topology, set-theoretic topology, algebraic topology and differential topology. In particular, instances of modern day topology are metrizability theory, axiomatic set theory, homotopy theory, and Morse theory. Topology also includes the now solved Poincaré conjecture and the controversial four color theorem, whose only proof, by computer, has never been verified by a human.
Geometry Trigonometry Differential geometry Topology Fractal geometry Measure Theory
Change
Understanding and describing change is a common theme in the natural sciences, and calculus was developed as a powerful tool to investigate it. Functions arise here, as a central concept describing a changing quantity. The rigorous study of real numbers and functions of a real variable is known as real analysis, with complex analysis the equivalent field for the complex numbers. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many problems lead naturally to relationships between a quantity and its rate of change, and these are studied as differential equations. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior.
Calculus Vector calculus Differential equations Dynamical systems Chaos theory Complex analysis
Structure
Many mathematical objects, such as sets of numbers and functions, exhibit internal structure. The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects. This is the field of abstract algebra. An important concept here is that of vectors, generalized to vector spaces, and studied in linear algebra. The study of vectors combines three of the fundamental areas of mathematics: quantity, structure, and space. A number of ancient problems concerning Compass and straightedge constructions were finally solved using Galois theory.
Number theory Abstract algebra Group theory Order theory
Foundations and philosophy
In order to clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed. Mathematical logic includes the mathematical study of logic and the applications of formal logic to other areas of mathematics; set theory is the branch of mathematics that studies sets or collections of objects. Category theory, which deals in an abstract way with mathematical structures and relationships between them, is still in development. The phrase "crisis of foundations" describes the search for a rigorous foundation for mathematics that took place from approximately 1900 to 1930.[33] Some disagreement about the foundations of mathematics continues to present day. The crisis of foundations was stimulated by a number of controversies at the time, including the controversy over Cantor's set theory and the Brouwer-Hilbert controversy.
Mathematical logic is concerned with setting mathematics on a rigorous axiomatic framework, and studying the results of such a framework. As such, it is home to Gödel's second incompleteness theorem, perhaps the most widely celebrated result in logic, which (informally) implies that any formal system that contains basic arithmetic, if sound (meaning that all theorems that can be proven are true), is necessarily incomplete (meaning that there are true theorems which cannot be proved in that system). Gödel showed how to construct, whatever the given collection of number-theoretical axioms, a formal statement in the logic that is a true number-theoretical fact, but which does not follow from those axioms. Therefore no formal system is a true axiomatization of full number theory.[citation needed] Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science.
Mathematical logic Set theory Category theory
Discrete mathematics
Discrete mathematics is the common name for the fields of mathematics most generally useful in theoretical computer science. This includes, on the computer science side, computability theory, computational complexity theory, and information theory. Computability theory examines the limitations of various theoretical models of the computer, including the most powerful known model – the Turing machine. Complexity theory is the study of tractability by computer; some problems, although theoretically solvable by computer, are so expensive in terms of time or space that solving them is likely to remain practically unfeasible, even with rapid advance of computer hardware. Finally, information theory is concerned with the amount of data that can be stored on a given medium, and hence deals with concepts such as compression and entropy.
On the purely mathematical side, this field includes combinatorics and graph theory.
As a relatively new field, discrete mathematics has a number of fundamental open problems. The most famous of these is the "P=NP?" problem, one of the Millennium Prize Problems.[34]
Combinatorics Theory of computation Cryptography Graph theory
Applied mathematics
Applied mathematics considers the use of abstract mathematical tools in solving concrete problems in the sciences, business, and other areas.
Applied mathematics has significant overlap with the discipline of statistics, whose theory is formulated mathematically, especially with probability theory. Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data be available). When reconsidering data from experiments and samples or when analyzing data from observational studies, statisticians "make sense of the data" using the art of modelling and the theory of inference – with model selection and estimation; the estimated models and consequential predictions should be tested on new data.[35]
Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using ideas of functional analysis and techniques of approximation theory; numerical analysis includes the study of approximation and discretization broadly with special concern for rounding errors. Other areas of computational mathematics include computer algebra and symbolic computation.
Mathematical physics
Fluid dynamics
Numerical analysis
Optimization
Probability theory
Statistics
Financial mathematics
Game theory
Mathematical biology
Mathematical chemistry
Mathematical economics
Control theory
Geometry Trigonometry Differential geometry Topology Fractal geometry Measure Theory
Change
Understanding and describing change is a common theme in the natural sciences, and calculus was developed as a powerful tool to investigate it. Functions arise here, as a central concept describing a changing quantity. The rigorous study of real numbers and functions of a real variable is known as real analysis, with complex analysis the equivalent field for the complex numbers. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many problems lead naturally to relationships between a quantity and its rate of change, and these are studied as differential equations. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior.
Calculus Vector calculus Differential equations Dynamical systems Chaos theory Complex analysis
Structure
Many mathematical objects, such as sets of numbers and functions, exhibit internal structure. The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects. This is the field of abstract algebra. An important concept here is that of vectors, generalized to vector spaces, and studied in linear algebra. The study of vectors combines three of the fundamental areas of mathematics: quantity, structure, and space. A number of ancient problems concerning Compass and straightedge constructions were finally solved using Galois theory.
Number theory Abstract algebra Group theory Order theory
Foundations and philosophy
In order to clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed. Mathematical logic includes the mathematical study of logic and the applications of formal logic to other areas of mathematics; set theory is the branch of mathematics that studies sets or collections of objects. Category theory, which deals in an abstract way with mathematical structures and relationships between them, is still in development. The phrase "crisis of foundations" describes the search for a rigorous foundation for mathematics that took place from approximately 1900 to 1930.[33] Some disagreement about the foundations of mathematics continues to present day. The crisis of foundations was stimulated by a number of controversies at the time, including the controversy over Cantor's set theory and the Brouwer-Hilbert controversy.
Mathematical logic is concerned with setting mathematics on a rigorous axiomatic framework, and studying the results of such a framework. As such, it is home to Gödel's second incompleteness theorem, perhaps the most widely celebrated result in logic, which (informally) implies that any formal system that contains basic arithmetic, if sound (meaning that all theorems that can be proven are true), is necessarily incomplete (meaning that there are true theorems which cannot be proved in that system). Gödel showed how to construct, whatever the given collection of number-theoretical axioms, a formal statement in the logic that is a true number-theoretical fact, but which does not follow from those axioms. Therefore no formal system is a true axiomatization of full number theory.[citation needed] Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science.
Mathematical logic Set theory Category theory
Discrete mathematics
Discrete mathematics is the common name for the fields of mathematics most generally useful in theoretical computer science. This includes, on the computer science side, computability theory, computational complexity theory, and information theory. Computability theory examines the limitations of various theoretical models of the computer, including the most powerful known model – the Turing machine. Complexity theory is the study of tractability by computer; some problems, although theoretically solvable by computer, are so expensive in terms of time or space that solving them is likely to remain practically unfeasible, even with rapid advance of computer hardware. Finally, information theory is concerned with the amount of data that can be stored on a given medium, and hence deals with concepts such as compression and entropy.
On the purely mathematical side, this field includes combinatorics and graph theory.
As a relatively new field, discrete mathematics has a number of fundamental open problems. The most famous of these is the "P=NP?" problem, one of the Millennium Prize Problems.[34]
Combinatorics Theory of computation Cryptography Graph theory
Applied mathematics
Applied mathematics considers the use of abstract mathematical tools in solving concrete problems in the sciences, business, and other areas.
Applied mathematics has significant overlap with the discipline of statistics, whose theory is formulated mathematically, especially with probability theory. Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data be available). When reconsidering data from experiments and samples or when analyzing data from observational studies, statisticians "make sense of the data" using the art of modelling and the theory of inference – with model selection and estimation; the estimated models and consequential predictions should be tested on new data.[35]
Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using ideas of functional analysis and techniques of approximation theory; numerical analysis includes the study of approximation and discretization broadly with special concern for rounding errors. Other areas of computational mathematics include computer algebra and symbolic computation.
Mathematical physics
Fluid dynamics
Numerical analysis
Optimization
Probability theory
Statistics
Financial mathematics
Game theory
Mathematical biology
Mathematical chemistry
Mathematical economics
Control theory
history of math
The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,[11] was probably that of numbers: the realization that two apples and two oranges (for example) have something in common.
In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time – days, seasons, years.[12] Elementary arithmetic (addition, subtraction, multiplication and division) naturally followed.
Further steps needed writing or some other system for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.[citation needed] Numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.[citation needed] The Indus Valley civilization developed the modern decimal system, including the concept of zero.
Mayan numeralsThe earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time and nothing much more advanced until around 3000BC onwards when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, building and construction and astronomy.[13] The systematic study of mathematics in its own right began with the Ancient Greeks between 600 and 300BC.
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries have been made throughout history and continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."[14]
source:wiki
In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time – days, seasons, years.[12] Elementary arithmetic (addition, subtraction, multiplication and division) naturally followed.
Further steps needed writing or some other system for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.[citation needed] Numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.[citation needed] The Indus Valley civilization developed the modern decimal system, including the concept of zero.
Mayan numeralsThe earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time and nothing much more advanced until around 3000BC onwards when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, building and construction and astronomy.[13] The systematic study of mathematics in its own right began with the Ancient Greeks between 600 and 300BC.
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries have been made throughout history and continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."[14]
source:wiki
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
Fractions
Digits 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.
source:math.com
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
Fractions
Digits 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.
source:math.com
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