Real Number
Using Complex Numbers In Circuit Analysis
Numbers And Numbers Essay
Artifact Relating To Numbers Essay
Importance Of Oral And Written Names For Numbers
Index Numbers
Everything about the Number Zero
Number 1-10 Relationships
Roman Numeral System
Significance Of The Number Seven In Poetry
Article Of Numbers Analysis
How Are Roman Numbers Used In Todays World
Notes On Integers And Integers Essay
Just Numbers In E. B. Whites About Myself
Numbers In Macbeth
The Importance of Numbers in Chemistry
Number Theory Outcast Analysis
1. Real Number
In mathematics, a real number is a value that represents a quantity along a continuous line. The real
numbers include all the rational numbers, such as the integer в€’5 and the fraction 4/3, and all the
irrational numbers such as в€
љ2 (1.41421356... the square root of two, an irrational algebraic
number) and ПЂ (3.14159265..., a transcendental number). Real numbers can be thought of as points
on an infinitely long line called the number line or real line, where the points corresponding to
integers are equally spaced. Any real number can be determined by a possibly infinite decimal
representation such as that of 8.632, where each consecutive digit is measured in units one tenth the
size of the previous one. The real line can be thought of as a...show more content...
More formally, real numbers have the two basic properties of being an ordered field, and having
the least upper bound property. The first says that real numbers comprise a field, with addition and
multiplication as well as division by nonzero numbers, which can be totally ordered on a number
line in a way compatible with addition and multiplication. The second says that if a nonempty set of
real numbers has an upper bound, then it has a least upper bound. The second condition
distinguishes the real numbers from the rational numbers: for example, the set of rational numbers
whose square is less than 2 is a set with an upper bound (e.g. 1.5) but no least upper bound: hence
the rational numbers do not satisfy the least upper bound property.
In physics
In the physical sciences, most physical constants such as the universal gravitational constant, and
physical variables, such as position, mass, speed, and electric charge, are modeled using real
numbers. In fact, the fundamental physical theories such as classical mechanics, electromagnetism,
quantum mechanics, general relativity and the standard model are described using mathematical
structures, typically smooth manifolds or Hilbert spaces, that are based on the real numbers
although actual measurements of physical quantities are of
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2. Using Complex Numbers In Circuit Analysis
Complex Analysis:
Complex analysis, traditionally known as the theory of functions of a complex variable, is the
branch of mathematical analysis that investigates functions of complex numbers. It is useful in
many branches of mathematics, including algebraic geometry, number theory, applied mathematics;
as well as in physics, including hydrodynamics and thermodynamics and also in engineering fields
such as nuclear, aerospace, mechanical and electrical engineering.
Murray R. Spiegel described complex analysis as "one of the most beautiful as well as useful
branches of Mathematics".
Using Complex Numbers in Circuit Analysis:
The purpose of this note is to review the algebra of concept numbers and show how they can be
used to simplify analyses...show more content...
Take a look at the equations in the previous section. The addition and subtraction equations do not
mix up the real and imaginary parts, but the equations for multiplication and division do. Multiplying
a complex number by a real constant also obviously does not mix up the real and imaginary parts.
Essentially, a linear equation is one that will not mix up the real and imaginary parts of the voltages
and currents. From a practical standpoint, a linear circuit is one that includes only passive
components (resistors, capacitors, and inductors) plus voltage and/or current sources. No diodes,
transistors, vacuum tubes, etc. are allowed. It is perhaps worth mentioning here that the same
formalism, with the same advantages of using complex numbers, works in mechanics when dealing
with small, harmonic oscillations of mechanical systems. voe^(j(wt)) or Io e^(j(wt)) where the
phase can be taken to be zero if there is only one source. Otherwise the relative phases of the sources
must be taken into account. Then treat each passive component as an impedance
Resistor: Z = R
Capacitor
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3. Numbers And Numbers Essay
Numbers, Numbers and Numbers
I have been always treated as a geek! Having a unique childhood in eastern society. The story begins
when my close friend and cousin, Mohamed who is a software engineer, told dady that he ought to
buy me that magnificent invention the computer. Mohamed also told dady that my ability to learn is
notable and my rapid response to commands is abnormal.
Dady bought me my lovely computer when I was only 3 years old. Mom and Dad paid a lot of
attention to me as I was the first–born child in our small family; "I was always putting your tiny
hands on the mouse and the keyboard to get used to them" said my mother. But having a computer
will not satisfy a curious kind of person like me, I remember uncovering each pen I have to
discover how it works, trying to open the control panel to figure out why dad always warned me not
to open it and trying to play with it .eventually, curiosity led to discover what beyond my lovely
machine: Codes....show more content...
The way I solve math indicated how passionate I am. But I want to deal with more and more
numbers!. Intelligent people always impressed me as well as codes! After dealing with java basics
and Algorithm, I found computer science portrays me .
Complier is skillful so as me
During my primary school , I achieved many awards like the best student for 1 year and ranked the
first academically for the whole primary stage. My teacher in Grade 5 told my parents one day
that I finish my exams before anyone else , this was weird according to hard exam I took ,
However I got high marks . My parents cared lot about my marks although what I cared about was
my math grades and my process. During the breaks between sessions I used to read national
geographic magazine just to read about the modern invention and technology. My curiosity helped to
finish a complete course in Photoshop.
Smart as a
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4. Artifact Relating To Numbers Essay
Numbers are an extremely important part of our everyday life. They have been around for a long
time, but how long, exactly? The earliest artifact relating to numbers is a bone with scratch marks
on it from 150,000 years ago. Actual numbers seem to have started around 500 BCE in India. This
was because Indians needed very precise numbers for trading and building. Indians were one of the
first to write their numbers, to create decimals and use them, and to use the number zero.The
numbers that the Indians created are known as Arabic numerals. Archimedes was very interested in
mathematics. He was very curious and tried to discover things like how many grains of sand there
were in the entire universe. Later in history, Archimedes exercises helped
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5. Importance Of Oral And Written Names For Numbers
Oral and Written Names for Numbers: This section is focusing on connecting oral and written names
for numbers with base–ten concepts by using groups of tens or hundreds for counting. It is essential
to remember that saying and writing numbers are conventions instead of concepts, and students are
learning this by being told instead problem–based activities. It is especially important to remember
that these conventions or patterns may be different for English Langauage Learners.
Two–Digit Number Names: For two–digit numbers, it is best to start with base ten materials and
language, because when they go to writing it will be easier to transfer, otherwise they may write 52
as 502 because of how it said. It is much easier to go from base ten language to the standard
language.
Three–Digit Number Names: As the numbers increase in size, there tends to be an increase in
mistakes, but to avoid mistakes, it is essential that you vary use of base–ten language and standard
language. It is also helpful to only change one place value at a time. Another way to help students is
to show them counterexamples and then have them correct the example. Numbers with no tens
usually leads to major confusion, and this is where base–ten language will help, but avoid calling
zero a placeholder because it does contain value.
Written Symbols: When starting to teach the students on how to write the names out, there are
Place–Value mats and Place–Value Cards. These two methods are more effective when
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6. Communicating Through Numbers in Beloved
Humanity uses numbers as a way to communicate beyond words, evoking ideas more readily than
words alone are able to. All religions and cultures have significant numbers that communicate an
essence or idea more quickly and completely than words can. It is in this manner that Toni Morrison
uses numbers in Beloved. Significant numbers occur starting with the first symbols of the text and
the words on the pages before the body of the text starts.
124. The first thing to appear, and we already have a significant number. Sethe has four children. The
third one is dead. Numbers 1, 2, and 4 remain. Another number that stands alone in its significance is
twenty–eight. Twenty–eight...show more content...
Rather than tell Sethe with words that trying to kill her children was inhuman, Paul D uses
numbers: "You got two feet, Sethe, not four" (165). There are thirty women that arrive to remove
Beloved. Thirty is a symbol of justice and order, according to Marianne Schimmel. When
schoolteacher arrives with his party, they are described as "the four horsemen" (148). In fact, the
only time a number occurs by itself as a sentence is to describe them: "All the while it was coming
down the road. Four. Riding close together, bunched–up like, and righteous" (157). Each of these is a
powerful symbol, though none of these numbers recur in the text, at least not with these meanings.
Two is duality, a pair, a division. It is also a unity, two halves of the same whole. Sex is expressed in
many cultures as a duality, the yin and yang, father sky and mother earth. In Beloved, twos, fours,
and even twenties occur in situations related to sex and children. Baby Suggs has eight children
(209), four girls, four boys. Sethe has four. Two boys, two girls. 124 has two stories, and Sethe
and Paul D have sex on the second floor. At Mrs. Garner's wedding, they ate four sheep (59). From
the two buckets of blackberries he picked, Stamp Paid put two into the mouth of four week old
Denver (170). At Baby Suggs' revival, after talking about "your life–holding womb and your
life–giving private parts," the crowd sings in "four–part harmony" (89). Such a performance
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7. Index Numbers
Importance of Index Number in Business Introduction:
An index number is a statistical device for comparing the general level of magnitude of a group
of related variables in two or more situation. If we want to compare the price level of 2000 with
what it was in 1990, we shall have to consider a group of variables such as price of wheat, rice,
vegetables, cloth, house rent etc., if the changes are in the same ratio and the same direction; we
face no difficulty to find out the general price level. But practically, if we think changes in different
variables are different and that too, upward or downward, then the price is quoted in different units
i.e milk for litre, rice or wheat for kilogram, rent for square feet, etc We want one figure to...show
more content...
Consumer Price Index
Consumer Price index is also called the cost of living index. It represents the average change over
time in the prices paid by the ultimate consumer of a specified basket of goods and services. A
change in the price level affects the costs of living of different classes of people differently. The
general index number fails to reveal this. So there is the need to construct consumer price index.
People consume different types of commodities. People' s consumption habit is also different
from man to man, place to place and class to class i.e richer class, middle class and poor class. The
scope of consumer price is necessary, to specify the population group covered. For example,
working class, poor class, middle class, richer class, etc and the geographical areas must be covered
as urban, rural, town, city etc.
Use of Consumer Price index
The consumer price indices are of great significance and are given below.
1. This is very useful in wage negotiations, wage contracts and dearness allowance adjustment in
many countries.
2. At government level, the index numbers are used for wage policy, price policy, rent control,
taxation and general economic policies.
3. Change in the purchasing power of money and real income can be measured.
4. Index numbers are also used for analyzing market price for particular kinds of goods and services.
Following are the main uses:
A Barometer:
Index numbers serve as a barometer for measuring the value of money. With the help of
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8. In engineering studies, working with numbers is one of the most substantial concepts. Numbers are
not used only in civil or architecture engineering as most of people think. Numbers are important in
all engineering disciplines. For example, agriculture engineers work in numbers in there calculation
to design systems that produce food, feed, fiber and other products with high quality. Also, in
computer engineering field, computer engineers must know how to deal with numbers because
computer language based on numbers. For this reason, this section will describe the mechanisms of
using numbers in a proper way.
Numbers notation is a way that scientist used to reformat numbers especially, very large numbers
and vary small numbers. Numbers notation has many useful properties, so it used by scientist,
mathematicians, and engineers. (a x 10^b) is the form of all numbers written in scientific notation
,where b is an integer number , and a is real number . Also, we can read as 'a' times 10 raised to
power b. However, any number can be written in scientific notation (ax10) .for any number greater
than 1 the exponent b is positive. Otherwise, when number between 0 & 1 the exponent b is
negative and it can be written as ( ax10^–b). For example 0.0015 can be written as .5 x 10^–3.
When performing a mathematical calculation, it is important to pay attention to accuracy. Suppose
you are asked to measure the width of a standard piece of paper such as a page in this research . The
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9. Everything about the Number Zero
Quick Facts About Zero Zero is created to be used in many ways, and one of these ways is a
placeholder for an empty spot. This can be seen in the number 405 as it has no number in the tens
place but there is still a zero there to hold the place; otherwise it would be 45 and that is clearly
not the same as 405. On a date translated to be 876, a tablet was written on that was about the town
Gwalior where they planted a garden 187 by 270 hastas that produced enough flowers to create
50 garlands a day. In both the numbers 270 and 50 the zero is made very close to how they are
made today. A mathematician named Brahmagupta attempted to create arithmetic rules involving
zero and negative numbers. Rules like this one "The sum of zero and a negative number is
negative, the sum of a positive number and zero is positive, the sum of zero and zero is zero." He
was one of the first men to work and create rules about zero that we use today. Why You Cannot
Divide By Zero Zero can be a very problematic number in math. One of these problems is when one
would try to divide by zero. A way to explain why this can't happen is to think about the number we
are trying to divide as a pie. Dividing it by Đ’Đ… would give you 2 parts of the pie. If you divided it by
.1 would give you ten parts and so on. Trying to divide it by zero would leave you with infinite
parts, which doesn't work, as infinity is not a number but a concept. Imagine we could divide by
zero and get infinity we would
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10. Number 1-10 Relationships
According to the textbook "Elementary and Middle School Mathematics: Teaching Developentally",
the three important types of relationships for number 1 through 10 include; "one to two more; one
and two less, benchmarks between numbers from 5–10, and part–part–whole relationships".
The one to two more; one and two less concentrate the ideas of adding a number higher and one less
than the given number. For example; if given the number 5, the number one more is 6, and less than
5 is 4. An activity to help promote mathematical students would allow them to use "six dot cards".
This could reinforce the idea and allow students to visually see the steps.
Benchmarking numbers 5 and 10 focuses on middle numbers and breaking apart numbers to get the
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11. Roman Numeral System
Roman Numeral System
Origin: Roman numerals were created some time between 900s and 800s B.C. in ancient Rome.
The Roman numerals were created as a type of counting method, which was needed for trade.
Because trade was getting bigger, the Roman Numerals became a big help when they needed to add
and subtract their profits and such. The Roman Numerals used to just be one symbol each. For
example, I, V, X, L, C, D, M are seven symbols that were the independent symbols. I is 1, V is 5, X
is 10, L is 50, C is 100, D is 500, and M is 1000.
Rule: There are about four different rules that ties into the Roman numeral system. The first rule is
that a letter will be repeated for the amount that it is. For example, if you had a number like 30, in
Roman Numerals, it would be XXX because X is equal to 10 and there are three X's. However, a
letter can only be repeated up to three times. The second rule, for Roman Numerals, is that you
must add the amount that is placed after another letter, if it is greater than the letter placed in
front of it. For example, VI is equal to 6 because 5(V) plus 1(I) is 6. Another example would be
MCC. MCC is 1200 because 1000(M) plus 100(C) plus 100(C) are equal to 1200. The third rule is
that a letter must be subtracted if it is placed before another letter with greater value. For example,
IV is equal to 4 because 5(V) minus 1(I) equals 4. There are actually more rules for subtracting the
amounts of Roman Numerals. You can only subtract powers of ten like
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12. Significance Of The Number Seven In Poetry
Before being used by human beings as scientific symbols, the numbers played a symbolic and
mythological role in human life. The connection between the life of the primitive man with the
numbers has certainly been more, if not less, than today. In the current study, the number 7 has
been considered as one of the most efficient mythological symbols and archetypes in the
contemporary poetry to investigate into the role of this mythological number in the perspective of
contemporary poets. The number seven is a symbol of perfection and a combination of three and
four. Three is a symbol of female and four is a symbol of male and that's why it has drawn a lot of
attention. Many of the symbolic and ancient roles of this number are still used in the subconscious
of today's human beings. The contemporary poets have used the number seven in their poems as a
sacred and complete number, the number of the...show more content...
104). As stated by Cassirer, in the Greek philosophy, the number seven belongs to the virgin Athena
who has not been born from a mother and the number seven represents god. Also, in the Middle
Ages, they regarded the number seven as a complete number. Of course, "from the same early times,
the number nine has been in competition with the number seven. In the myths and creeds of the
Greek, and also in the beliefs of the Germans, there have been nine distances/ intervals similar to the
periods of seven distances/intervals." (Cassirer, 1999, P. 233). In the Golden Branch, Frazer (1384,
P. 268) refers to the myths about the numbers seven and nine and their sanctity and mentions that the
tribe witches or the doctors cured the pain or the fever of the patient by tying a thread to the patient's
body with seven or nine knots and unknotting each one every
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13. Numerology in The Odyssey
"Everything is named or numbered, but few people are conscious of the degree to which names and
numbers influence their experience, progress, and communication," declared Juno Jordan, the
"grandmother" of numerology (qtd. in Lagerquist and Lenard 4). Numerology, the language of
numbers and moreover the study of how they relate to our lives, speaks about the hidden worlds
contained within the simplest numbers. Numerology attempts to analyze numerical information, and
makes a determination of the implications and associations that these numbers have (Kelly 10). This
metaphysical science has its roots in the ancient cultures of Greece, Rome, and Egypt, and also has
ties to the Hebrew Kabbalah; it has unlocked the...show more content...
This number is related to people who work better when part of a duo instead of as a member of a
group, or even all alone (Heyss 32). This number represents cooperation and as a result is often
associated in literature with people who are best when working for and interacting with other
people. There are several occasions in which Homer uses the number two when speaking of such
people as servants who are cooperative and are therefore reliable workers. One such occasion is in
Odysseus 's instructions to his companions on the island of the Lotus–Eaters in which he sends two
men to accompany the herald in learning about the island and its inhabitants (Homer 9.90–93). There
is yet another situation in which two handmaidens accompany and attend Penelope when she
appeared before the suitors (Homer 18.206–207). Nausikaa also slept beside two handmaidens who
lay on either side of the bedpost (Homer 6.17–19) and moreover Melanthios, driving the goats which
would be the suitor 's dinner, was followed by two herdsmen (Homer 20.173–175). Such duos, as
can be seen by those presented by Homer, prefer to have somebody around to tell them what to do –
a portrayal of the meaning of the number two.
The number three represents synthesis and essence; it 's influence is evident in almost all religions
and philosophies, as well as in mythology (Heyss 34). The number three is embedded in the
symbolism of many powerful trinities: the Maiden, Mother and
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14. Article Of Numbers Analysis
The article of Numbers informs us of how people relate in different environments. Depending on
who they are and what role they may be playing at a given time may change how others perceive
them; either consciously or subconsciously. People that fall in these categories act one way, and in
turn have the people in the opposite category act in another way. In Kanter's article, she refers to
Georg Simmel's analysis of the significance of the number of people within a group and the four
groups that account for these in an organization. Simmel names these groups uniform, skewed,
tilted and balanced. If the number of people of a certain social type change in a group, that can
change the social interaction within groups. The Uniform group has people of the same social type.
This can include race, sex or ethnicity. The Uniform ratio is 100:0. Skewed...show more content...
Where men are usually doctors, we have men that are also nurses or customer service
representatives. The few men that I have worked with have been very nice and easy going. One
thing that makes it easier in a skewed group of females versus males is that when a patient says
that it was a male that they spoke to, we can pretty much narrow it down quickly. The men usually
realize that they are a "token" and can have fun with it. I haven't felt that there was any
resentment towards the tokens or vice versa. I don't believe every idea that Kanter has is
completely accurate. I have not noticed that the tokens felt out of place or stated so. Conclusion
Kanter's article is mostly about men to women ratio. This may have changed my own personal,
skewed comparison if it was about something else. Of course, there could be different scenarios if
the discussion was about different employment positions, or family dynamics. As I am sure some of
these examples in the article are accurate, I believe they are on the higher end of the spectrum of
being an abnormal way of treating one
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15. How Are Roman Numbers Used In Today's World
Roman numbers are used in many different ways in today's world. Roman numerals came about
because Romans needed a way to indicate numbers. Roman numerals were also used to indicate
the names of rulers and church leaders that have the same name. Roman numerals are represented
by seven letters: I, V, X, L, C, D and M. These letters represent the numbers 1, 5, 10, 50, 100, 500
and 1,000. The Romans didn't like four of the same numerals to be written in a row, so they
developed a system of subtraction. A single line, or "I," referred to one unit or finger; the "V"
represented five fingers, specifically, X equaled two hands. The numbers are placed from left to
right, and the order determines whether you add or subtract the values. If the smaller
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16. Notes On Integers And Integers Essay
3 NUMBERS
Real Numbers: Real numbers are all numbers that can be represented in a number line.
Natural Numbers: Natural numbers are all counting numbers such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, ...
Whole Numbers: Whole numbers are all positive numbers and zero such as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, ...
Integers: Integers are all positive and negative numbers and zero such as ...–12, –11, –10, –9, –8, –7,
–6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
Rational Numbers: Rational numbers are all integers and fractions.
Irrational Numbers: Irrational numbers are numbers that cannot be written as fractions such as в€
љ3
or ПЂ
Prime Numbers: Prime numbers are divisible only by 1 and itself such as 2, 3, 5, 7, 11, ...
Composite Numbers: Composite numbers are positive integers which are not prime, with factors
other than 1 and itself such as 4, 6, 8, 9, 10, 12, ...
Cardinal Numbers: Cardinal numbers are natural numbers used in counting such as 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, ...
Ordinal Numbers: Ordinal numbers describes the numerical position of an object or number such as
first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, ...
Even Numbers: Even numbers are numbers that can be evenly divided by 2 such as 2, 4, 6, 8, 10,
12, ...
PRACTICE 3A: Below, practice writing the definition of whole numbers to the best of your ability
(continue practicing until mastered).
4 NUMBER LINE
Number Line: A line which consists of
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17. Just Numbers In E. B. White's About Myself
E.B. White, a nineteenth–century writer, addresses the issue that we are all just numbers in his
paper "About Myself." White creatively uses tools such as comparison and syntax to prove that we
are much more. E.B. White uses numbers throughout his whole paper to make the point that we are
not just a number. When talking about his everyday activities he says, "I brush my hair with
Whiting–Adams Brush Number 010." White is comparing how household tools are given a
number just like us. He talks about how several of the things we use every day, like out combs,
nose spray, and pills, are all numbered just like us. White does this to show that we are not like
these objects, we are so much more. He is also showing that these products get their
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18. Numbers In Macbeth
Shakespeare is known throughout the world for amazing work, he is known for begin English poet,
playwright, and actor. One of the things that are astonishing about him would his plays some of the
most famous ones would be Macbeth, Hamlet, and, of course, the infamous Romeo and Juliet, but
what makes his work more astonishing would the usage of symbols and numbers that seem to
appear in ever play we read. Shakespeare tends to use numbers and symbols throughout Macbeth for
example and express in more detail his usage of symbols and numbers would be the usage of blood
and darkness and the number 3. What is the reason why Shakespeare uses these type of motifs in
Macbeth?
Macbeth is one of the most common types of play that show ambitions...show more content...
Numbers are also another form of symbols they might not have a strong impact on this play at all,
but Shakespeare tends to use the number 3 a lot, but when we tend to read we overlook or we
don't knownlogic these so call number reference they may be small detail, but usage of the
number 3 is clear and very well placed. The number three is also used in the Bible there are many
moments in the that we clearly see the used of three, for example, the Bible states Jesus prayed
three times in the Garden of Gethsemane before his arrest and it also states Three is the number of
resurrection. Christ was dead for three full days and three full nights. There are also other numbers
that the Bible uses like for example the number 6,7,12 also have a significant impact on life. In
Macbeth we see some references to three there redundant, but they are used for example the book
starts off with introducing the three witches aka creepy sisters that tell Macbeth future and also
throughout the book they're three murders in which Macbeth is amused to be main suspect those
murders of which would be the death of Banquo, Lady Macduff and Duncan. Some people tend to
believe that bad luck comes in three. Which can be superstishes, but everyone has their own
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19. The Importance of Numbers in Chemistry
In chemistry, numbers are very important in making calculations as well as collecting and recording
data. Because numbers are so prevalent in this field of study, many chemists find it important to use
very precise numbers. Their best way of doing so is through significant figures. The significant
figures for any number are the numbers that carry meaning contributing to that numbers precision. In
order for a number to be significant, it must follow a series of rules. For example, only zeroes that
are between two non–zero numbers or zeroes that both are to the right of a decimal and follow a
number greater than zero can be considered significant figures. In addition, any number greater than
zero is considered a significant figure, despite where it is located in a numerical value. These rules
that help clarify the significant figures of a value are just a few of the many rules that pertain to
significant figures. When it comes to calculations, the rules for the number of significant figures a
product or quotient can have, differs from those of the number of significant figures a sum or
difference can. In multiplication and division calculations, the product and quotient are expected to
be rounded to the same number of significant figures as the least precise piece of data in the
calculation. In addition and subtraction, the sum and difference are expected to be rounded to the
same number of decimal places as the least precise piece of data. In any calculation, the significant
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20. Number Theory Outcast Analysis
In the number theory podcast it is discussed how we go from twenty and four to twenty four. Bob
and Mike also discuss why we say it the way we say it. I personally like the feeling of saying
twenty four rather than twenty and four. It sounds more appropriate and grammatical. Bob and
Mike speak about how in old English they wrote "twenty and four" and even "four and twenty". But,
in modern english the and is eliminated and we pronounce it "twenty four". The conjunction and is
eliminated. The modern way arises randomly. The change came due to "laziness" according to Bob.
The easier approach took over universally. It is more natural to write the higher number first rather
than the lower. Lower before higher delays comprehension also according
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