10.7 Summary of key concepts

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module reviews the key concepts from the chapter "Signed Numbers."

Variables and constants ( [link] )

A variable is a letter or symbol that represents any member of a set of two or more numbers. A constant is a letter or symbol that represents a specific number. For example, the Greek letter $\pi$ (pi) represents the constant 3.14159 . . . .

The real number line ( [link] )

The real number line allows us to visually display some of the numbers in which we are interested.

Coordinate and graph ( [link] )

The number associated with a point on the number line is called the coordinate of the point. The point associated with a number is called the graph of the number.

A real number is any number that is the coordinate of a point on the real number line.

Types of real numbers ( [link] )

The set of real numbers has many subsets. The ones of most interest to us are:
The natural numbers : {1, 2, 3, 4, . . .}
The whole numbers : {0, 1, 2, 3, 4, . . .}
The integers : {. . . ,-3,-2,-1,0, 1, 2, 3, . . .}
The rational numbers : {All numbers that can be expressed as the quotient of two integers.}

Positive and negative numbers ( [link] )

A number is denoted as positive if it is directly preceded by a plus sign (+) or no sign at all. A number is denoted as negative if it is directly preceded by a minus sign (–).

Opposites are numbers that are the same distance from zero on the number line but have opposite signs. The numbers $a$ and $-a$ are opposites.

$-\left(-a\right)=a$

Absolute value (geometric) ( [link] )

The absolute value of a number $a$ , denoted $\mid a\mid$ , is the distance from $a$ to 0 on the number line.

Absolute value (algebraic) ( [link] )

1. like signs , add the absolute values of the numbers and associate with the sum the common sign.
2. unlike signs , subtract the smaller absolute value from the larger absolute value and associate with the difference the sign of the larger absolute value.

$\text{0}+\left(\text{any number}\right)=\text{that particular number}$ .

Since adding 0 to any real number leaves that number unchanged, 0 is called the additive identity .

Definition of subtraction ( [link] )

$a-b=a+\left(-b\right)$

Subtraction of signed numbers ( [link] )

To perform the subtraction $a-b$ , add the opposite of $b$ to $a$ , that is, change the sign of $b$ and follow the addition rules ( [link] ).

Multiplication and division of signed numbers ( [link] )

$\left(+\right)\left(+\right)=\left(+\right)$ $\frac{\left(+\right)}{\left(+\right)}=\left(+\right)$ $\frac{\left(+\right)}{\left(-\right)}=\left(-\right)$
$\left(-\right)\left(-\right)=\left(+\right)$
$\left(+\right)\left(-\right)=\left(-\right)$ $\frac{\left(-\right)}{\left(-\right)}=\left(+\right)$ $\frac{\left(-\right)}{\left(+\right)}=\left(-\right)$
$\left(-\right)\left(+\right)=\left(-\right)$

what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
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