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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 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 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.

3 , 1 , 2557878 , 56 34 , 10 , 2 , 1 , - 5 , - 6 , 35 , - 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] .

Set diagram of all the real numbers R , the rational numbers Q , the integers Z and the natural numbers N . The irrational numbers are the numbers not inside the set of rational numbers. All of the integers are also rational numbers, but not all rationalnumbers are integers.

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 - 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 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.


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

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

Mathematicians use the symbol 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:

a b

where a and b are integers and b 0 .

The following are examples of rational numbers:

20 9 , - 1 2 , 20 10 , 3 15

Notation tip

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

Mathematicians use the symbol 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

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
is it a question of log
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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