# Review of past work  (Page 7/8)

 Page 7 / 8

In this example, the decimal point must go after the first 2, but since the number after the 9 is a 7, $a=3,00$ .

So the number is $3,00×{10}^{m}$ , where $m=8$ , because there are 8 digits left after the decimal point. So, the speed of light in scientific notation totwo decimal places is $3,00×{10}^{8}$  ms ${}^{-1}$ .

As another example, the size of the HI virus is around $1,2×{10}^{-7}$  m. This is equal to $1,2×0,0000001$  m, which is 0,00000012 m.

## Real numbers

Now that we have learnt about the basics of mathematics, we can look at what real numbers are in a little more detail. The following are examples of realnumbers and it is seen that each number is written in a different way.

$\sqrt{3},\phantom{\rule{1.em}{0ex}}1,2557878,\phantom{\rule{1.em}{0ex}}\frac{56}{34},\phantom{\rule{1.em}{0ex}}10,\phantom{\rule{1.em}{0ex}}2,1,\phantom{\rule{1.em}{0ex}}-5,\phantom{\rule{1.em}{0ex}}-6,35,\phantom{\rule{1.em}{0ex}}-\frac{1}{90}$

Depending on how the real number is written, it can be further labelled as either rational, irrational, integer or natural. A set diagram of the differentnumber types is shown in [link] .

## Non-real numbers

All numbers that are not real numbers have imaginary components. We will not see imaginary numbers in this book but they come from $\sqrt{-1}$ . Since we won't be looking at numbers which are not real, if you see a number you can be sure it is a realone.

## Natural numbers

The first type of numbers that are learnt about are the numbers that are used for counting. These numbers are called natural numbers and are the simplest numbers in mathematics:

$0,1,2,3,4,...$

Mathematicians use the symbol ${\mathbb{N}}_{0}$ to mean the set of all natural numbers . These are also sometimes called whole numbers . The natural numbers are a subset of the real numbers since every natural number is also a real number.

## Integers

The integers are all of the natural numbers and their negatives:

$...-4,-3,-2,-1,0,1,2,3,4...$

Mathematicians use the symbol $\mathbb{Z}$ to mean the set of all integers . The integers are a subset of the real numbers, since every integer is a real number.

## Rational numbers

The natural numbers and the integers are only able to describe quantities that are whole or complete. For example, you can have 4 apples, but what happens whenyou divide one apple into 4 equal pieces and share it among your friends? Then it is not a whole apple anymore and a different type of number is needed to describe the apples. This type of number is known as a rational number.

A rational number is any number which can be written as:

$\frac{a}{b}$

where $a$ and $b$ are integers and $b\ne 0$ .

The following are examples of rational numbers:

$\frac{20}{9},\phantom{\rule{1.em}{0ex}}\frac{-1}{2},\phantom{\rule{1.em}{0ex}}\frac{20}{10},\phantom{\rule{1.em}{0ex}}\frac{3}{15}$

## Notation tip

Rational numbers are any number that can be expressed in the form $\frac{a}{b};a,b\in \mathbb{Z};b\ne 0$ which means “the set of numbers $\frac{a}{b}$ when $a$ and $b$ are integers”.

Mathematicians use the symbol $\mathbb{Q}$ to mean the set of all rational numbers . The set of rational numbers contains all numbers which can be written as terminating or repeating decimals.

## Rational numbers

All integers are rational numbers with a denominator of 1.

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
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
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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