Transcript Scientific Notation

6.022 x 10
23

What is it, why do we need it and
how do we do it.
• How long would it take to
count to one million?
• How many atoms are in one
cup of water?
• What is the mass of the earth
in grams?
• What is the rest mass of a
single electron?
23 days.
• It might not seem like it
but a million is a big
number but small when
compared to other
much larger numbers in
science.
24,000,000,000,000,000,000,000,000
• One glass of water has that many
atoms in it. That is more atoms
than there are cups of water in all
the oceans.
sextillion septillion quintillion quadrillion trillion
billion
million
thousand
hundred
24,000,000,000,000,000,000,000,000
• One glass of water has that many
atoms in it. That is more atoms
than there are cups of water in all
the oceans.
6,000,000,000,000,000,000,000,000,000g
The mass of the earth!
The rest mass of a single electron!
0.000000000000000000000000000000911kg
Which number is easier to use?
0.000000000000000000000000000000911kg or 9.11x10-31kg
24,000,000,000,000,000,000,000,000g or 2.4 x1025
6,000,000,000,000,000,000,000,000,000g or 6 x10^27
Calculating the force of gravity the sun exerts on the earth.
(1989100000000000000000000000000)( 5972190000000000000000000)
Fg  (0.0000000000667)
( 149600000000)2
30
24
(1.9891x10 )( 5.97219x10 )
Fg  (6.67x10 )
11 2
( 1.496x10 )
-11
Multiplication and Division are easier!
6.022 x 10
23

An abbreviation for very large and very
small numbers in science.
1a) Identify five objects smaller than the eye can see.
1b) Briefly Describe what the object is.
1c) Express its size in scientific and standard notation.
2a) Find five objects bigger than the sun.
2b) Briefly Describe what the object is.
2c) Express its size in scientific and standard notation.
3) Is the sun a large object on astronomical scales?
4) What is scientific notation and why do we use it?
Click the Picture of a Link, if
that is Down Click Here.
Order of Magnitude: Using the scale of the universe app, what
order of magnitude do the following objects have in meters?
Express them in scientific notation and include a fact about them.
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
A Human Being
Titanic
Boeing 747
Hummingbird
Mitochondrion
A Blue Whale
Angel Falls
Tyrannosaurus Rex
String
Up Quark
Water Molecule
Mount Everest
Ant
Ganymede
Proxima Centauri
Observable Universe
•
•
•
•
•
•
•
•
Total Human Height
Sirius A
Kuiper Belt
Gomez’s Hamburger
Glucose
Tarantula Nebula
Andromeda Galaxy
A Light Year
ESTIMATE
• Height of School
• Telephone Pole
• Length of CT
• Distance of US
• Length of Mall
• Height of Holy Land
•
•
•
Diameter of Golf Ball
Length of Pencil
Thickness of Paper
The Number of Golf balls that
could fit:
• On a school bus.
• In a suitcase
• In our classroom
• In a bathtub
BINGO! Guess How Many Jelly
Beans are in the Jar and
Win it!
6.022 x 10
23

An abbreviation for very large and very
small numbers in science.
Some number written in the form A x 10B
one non-zero number to the left of a decimal point.
Move decimals left or right and count the spaces.
Moving Left = positive exponent (big numbers)
Moving right = negative exponent (small numbers)
100
1000
24,000
365,445
2
0.001
0.000001
0.0000904
5.03 x 106
4.3x10-8
1.
2.
3.
4.
Where is the decimal?
Where do I want it?
How far did I move it?
Negative or Positive?
1234
1,020,000
18,300
54,234,012
4 million
0.00109
0.0000000034
0.0000904
1/10
12 thousandth
2.345x109
3.03 x 108
2.1x10-6
9x10-31
Convert to Scientific Notation
Convert to Standard Notation
6.022 x 10
23

An abbreviation for very large and very
small numbers in science.
• Rule 1
• Example
• Rule 1
• Example
Multiply the leading numbers and add the exponents!
Calculating the force of gravity the sun exerts on the earth.
(1989100000000000000000000000000)( 5972190000000000000000000)
Fg  (0.0000000000667)
( 149600000000)2
30
24
(1.9891x10 )( 5.97219x10 )
Fg  (6.67x10 )
11 2
( 1.496x10 )
-11
6.67 x 1.9891 x 5.97219 x 10 (-11 + 30 + 24)
1.496 x 1.496 x 10 (11+11)
(3x108) x (6x101) =
(2.235x108) x (6.453x101) =
• Rule 2
• Example
• Rule 2
• Example
Divide the leading numbers and subtract the exponents!
(8x108)
(4x101) =
(3x104)
(6x107) =
(2x102) + (4x101) =
(2.5x104) + (4.4x103) =
Convert to same power.
Keep the exponent.
Add the leading numbers
(4.45x109) x (3.43x100) =
(2.5x105) x (3x106) =
(4x1013) x (3x102) =
(2x104) x (3.5x102) =
(2.5x104) - (4.4x103) =
(2x102) - (4x101) =
(3.6x105) + (4x106) =
(9x106) =
(3x104)
(9.34x106)
(3.85x104)
(4x104) =
(8x106)
=
(12x106)
(3x107)
=
Multiplying
Multiply the Leading numbers
Add the Exponents
Dividing
Divide the Leading numbers
Subtract the Exponents
Adding and Subtracting
Convert to same power.
Keep the exponent.
Add the leading numbers