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The number 0.00000000000047 is written with an arrow extending to another number: 00000000000004.7. An arrow tracking the movement of the decimal point runs underneath the number. Above the number a label on the number reads: 13 places right.

Be careful not to include the leading 0 in your count. We move the decimal point 13 places to the right, so the exponent of 10 is 13. The exponent is negative because we moved the decimal point to the right. This is what we should expect for a small number.

4.7 × 10 −13

Scientific notation

A number is written in scientific notation    if it is written in the form a × 10 n , where 1 | a | < 10 and n is an integer.

Converting standard notation to scientific notation

Write each number in scientific notation.

  1. Distance to Andromeda Galaxy from Earth: 24,000,000,000,000,000,000,000 m
  2. Diameter of Andromeda Galaxy: 1,300,000,000,000,000,000,000 m
  3. Number of stars in Andromeda Galaxy: 1,000,000,000,000
  4. Diameter of electron: 0.00000000000094 m
  5. Probability of being struck by lightning in any single year: 0.00000143

  1. 24,000,000,000,000,000,000,000  m 24,000,000,000,000,000,000,000  m 22  places 2.4 × 10 22  m

  2. 1,300,000,000,000,000,000,000  m 1,300,000,000,000,000,000,000  m 21  places 1.3 × 10 21  m

  3. 1,000,000,000,000 1,000,000,000,000 12  places 1 × 10 12

  4. 0.00000000000094  m 0.00000000000094  m 13  places 9.4 × 10 −13  m

  5. 0.00000143 0.00000143 6  places 1.43 × 10 −6

Write each number in scientific notation.

  1. U.S. national debt per taxpayer (April 2014): $152,000
  2. World population (April 2014): 7,158,000,000
  3. World gross national income (April 2014): $85,500,000,000,000
  4. Time for light to travel 1 m: 0.00000000334 s
  5. Probability of winning lottery (match 6 of 49 possible numbers): 0.0000000715
  1. $ 1.52 × 10 5
  2. 7.158 × 10 9
  3. $ 8.55 × 10 13
  4. 3.34 × 10 −9
  5. 7.15 × 10 −8

Converting from scientific to standard notation

To convert a number in scientific notation    to standard notation, simply reverse the process. Move the decimal n places to the right if n is positive or n places to the left if n is negative and add zeros as needed. Remember, if n is positive, the value of the number is greater than 1, and if n is negative, the value of the number is less than one.

Converting scientific notation to standard notation

Convert each number in scientific notation to standard notation.

  1. 3.547 × 10 14
  2. −2 × 10 6
  3. 7.91 × 10 −7
  4. −8.05 × 10 −12

  1. 3.547 × 10 14 3.54700000000000 14  places 354,700,000,000,000

  2. −2 × 10 6 −2.000000 6  places −2,000,000

  3. 7.91 × 10 −7 0000007.91 7  places 0.000000791

  4. −8.05 × 10 −12 −000000000008.05 12  places −0.00000000000805

Convert each number in scientific notation to standard notation.

  1. 7.03 × 10 5
  2. −8.16 × 10 11
  3. −3.9 × 10 −13
  4. 8 × 10 −6
  1. 703 , 000
  2. −816 , 000 , 000 , 000
  3. −0.000 000 000 000 39
  4. 0.000008

Using scientific notation in applications

Scientific notation, used with the rules of exponents, makes calculating with large or small numbers much easier than doing so using standard notation. For example, suppose we are asked to calculate the number of atoms in 1 L of water. Each water molecule contains 3 atoms (2 hydrogen and 1 oxygen). The average drop of water contains around 1.32 × 10 21 molecules of water and 1 L of water holds about 1.22 × 10 4 average drops. Therefore, there are approximately 3 ( 1.32 × 10 21 ) ( 1.22 × 10 4 ) 4.83 × 10 25 atoms in 1 L of water. We simply multiply the decimal terms and add the exponents. Imagine having to perform the calculation without using scientific notation!

Questions & Answers

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket 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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Selected topics in algebra. OpenStax CNX. Sep 02, 2015 Download for free at http://legacy.cnx.org/content/col11877/1.2
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