<< Chapter < Page Chapter >> Page >

0.000000000004632 = 4.632 × 10 12

The decimal point is twelve places to the right of its original position, and the power of 10 is 12 .

Got questions? Get instant answers now!

0.027 = 2.7 × 10 2

The decimal point is two places to the right of its original position, and the power of 10 is 2 .

Got questions? Get instant answers now!

Practice set a

Write the following numbers in scientific notation.

5387.7965

5.3877965 × 10 3

Got questions? Get instant answers now!

179,000,000,000,000,000,000

1.79 × 10 20

Got questions? Get instant answers now!

0.000098001

9.8001 × 10 5

Got questions? Get instant answers now!

0.000000000000000054

5.4 × 10 17

Got questions? Get instant answers now!

0.0000001

1.0 × 10 7

Got questions? Get instant answers now!

0.00000001

1.0 × 10 8

Got questions? Get instant answers now!

Scientific form to standard form

A number written in scientific notation can be converted to standard form by reversing the process shown in Sample Set A.

Converting from scientific notation

To convert a number written in scientific notation to a number in standard form, move the decimal point the number of places prescribed by the exponent on the 10.

Positive exponent negative exponent

Move the decimal point to the right when you have a positive exponent, and move the decimal point to the left when you have a negative exponent.

Sample set b

4.673 × 10 4 .

The exponent of 10 is 4 so we must move the decimal point to the right 4 places (adding 0 ' s if necessary).

Number written in scientific notation as 'four point six seven three zero multiplied by ten to the fourth power' is equal to 'forty six thousand seven hundred thirty' in standard form.

Got questions? Get instant answers now!

2.9 × 10 7 .

The exponent of 10 is 7 so we must move the decimal point to the right 7 places (adding 0 ' s if necessary).

2.9 × 10 7 = 29000000

Got questions? Get instant answers now!

1 × 10 27 .

The exponent of 10 is 27 so we must move the decimal point to the right 27 places (adding 0 ' s without a doubt).

1 × 10 27 = 1,000,000,000,000,000,000,000,000,000

Got questions? Get instant answers now!

4.21 × 10 5 .

The exponent of 10 is 5 so we must move the decimal point to the left 5 places (adding 0 ' s if necessary).

4.21 × 10 5 = 0 .0000421

Got questions? Get instant answers now!

1.006 × 10 18 .

The exponent of 10 is 18 so we must move the decimal point to the left 18 places (adding 0 ' s if necessary).

1.006 × 10 18 = 0.000000000000000001006

Got questions? Get instant answers now!

Practice set b

Convert the following numbers to standard form.

8.88 × 10 5

0.0000888

Got questions? Get instant answers now!

Working with numbers in scientific notation

Multiplying numbers using scientific notation

There are many occasions (particularly in the sciences) when it is necessary to find the product of two numbers written in scientific notation. This is accomplished by using two of the basic rules of algebra.

Suppose we wish to find ( a × 10 n ) ( b × 10 m ) . Since the only operation is multiplication, we can use the commutative property of multiplication to rearrange the numbers.

( a × 10 n ) ( b × 10 m ) = ( a × b ) ( 10 n × 10 m )

Then, by the rules of exponents, 10 n × 10 m = 10 n + m . Thus,

( a × 10 n ) ( b × 10 m ) = ( a × b ) × 10 n + m

The product of ( a × b ) may not be between 1 and 10, so ( a × b ) × 10 n + m may not be in scientific form. The decimal point in ( a × b ) may have to be moved. An example of this situation is in Sample Set C, problem 2.

Sample set c

( 2 × 10 3 ) ( 4 × 10 8 ) = ( 2 × 4 ) ( 10 3 × 10 8 ) = 8 × 10 3 + 8 = 8 × 10 11

Got questions? Get instant answers now!

( 5 × 10 17 ) ( 8.1 × 10 22 ) = ( 5 × 8.1 ) ( 10 17 × 10 22 ) = 40.5 × 10 17 22 = 40.5 × 10 5

We need to move the decimal point one place to the left to put this number in scientific notation.

Thus, we must also change the exponent of 10.

40.5 × 10 5 4.05 × 10 1 × 10 5 4.05 × ( 10 1 × 10 5 ) 4.05 × ( 10 1 5 ) 4.05 × 10 4

Thus,

( 5 × 10 17 ) ( 8.1 × 10 22 ) = 4.05 × 10 4

Got questions? Get instant answers now!

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
Please keep in mind that it's not allowed to promote any social groups (whatsapp, facebook, etc...), exchange phone numbers, email addresses or ask for personal information on QuizOver's platform.
QuizOver Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask