Transcript scientific notation - Mr-Hubeny

• IMAX Cosmic Voyage
• Link to the Powers of 10 portion of video.
– http://www.youtube.com/watch?v=qxXf7AJZ7
3A
Copyright © 2010 Ryan P. Murphy
• Link! Size Scale of the Universe (Flash)
– http://inciswf.com/589217_scale_of_universe_
enhanced.swf
• How many kilometers away from the earth
is the sun?
• Answer! 1.46 x 108
Copyright © 2010 Ryan P. Murphy
When to Use Scientific
Notation

Astronomically Large Numbers


Infinitesimally Small Numbers


mass of planets, distance between stars
size of atoms, protons, electrons
A number with “ambiguous” zeros

59,000
 HOW PRECISE IS IT?
Powers of 10

Positive Exponents
10  10
1
10  10  10  100
2
10  10  10  10  1000
3
10  10  10  10  10  10,000
4
Exponent of Zero Means “1”
100 = 1
Powers of 10

Negative Exponents
1
10  101  0.1
10
2
1
 101  101  100
 0.01
3
1
10  101  101  101  1000
 0.001
10
4
 101  101  101  101  10,1000  0.0001
Exponent of Zero Means “1”
100 = 1
Converting From Standard to
Scientific Notation




Move decimal until it is behind the first no zero number
(sig. fig.)
Power of 10 is the # of spaces the decimal moved
Decimal moves to the left, the exponent is positive
Decimal moves to the right, the exponent is negative

428.5

4.285 x 102
(decimal moves 2 spots left)

0.0004285

4.285 x 10-4
(decimal moves 4 spots right)
Converting From Scientific to
Standard Notation




Move decimal point
# of spaces the decimal moves is the power of 10
If exponent is positive, move decimal to the right
If exponent is negative, move decimal to the left

4.285 x 102

428.5
(move decimal 2 spots right)

4.285 x 10-4

0.0004285
(decimal moves 4 spots left)
• Activity! Practice Scientific Notation.
Copyright © 2010 Ryan P. Murphy
• Activity! Practice Scientific Notation.
– What is 567,000 in scientific notation?
Copyright © 2010 Ryan P. Murphy
• 567000
• 5.67000
• 5.67
• 567000
• 5.67000
• 5.67
• 567000
• 5.67000
• 5.67 x 105
• Activity! Scientific Notation Practice.
– What is 250,000 in scientific notation?
Copyright © 2010 Ryan P. Murphy
• 250,000 = 2.50000
Copyright © 2010 Ryan P. Murphy
• 250,000 = 2.50000
•
= 2.5 x 10_
Copyright © 2010 Ryan P. Murphy
• 250,000 = 2.50000
•
= 2.5 x 10_
Copyright © 2010 Ryan P. Murphy
• 250,000 = 2.50000
•
= 2.5 x 105
Copyright © 2010 Ryan P. Murphy
• 250,000 = 2.50000
•
= 2.5 x 105
Copyright © 2010 Ryan P. Murphy
Write the number:
• 154 x 102
15400
• 0.2844 x 106
284400
• 2.7 x 10-3
0.0027
• 599 x 10-2
5.99