# Review of past work  (Page 7/8)

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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 $3,00×{10}^{8}\phantom{\rule{3pt}{0ex}}m·s{}^{-1}$

As another example, the size of the HI virus is around $1,2×{10}^{-7}$  m. This is equal to $1,2×0,0000001\phantom{\rule{3pt}{0ex}}m$ , which is $0,00000012\phantom{\rule{3pt}{0ex}}m$ .

## 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 todescribe 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.

You can add and multiply rational numbers and still get a rational number at the end, which is very useful. If we have 4 integers $a,b,c$ and $d$ , then the rules for adding and multiplying rational numbers are

how can chip be made from sand
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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