Transcript Scientific Notation

Do First
Actions: Turn in metric conversion sheet and the
density lab.
Questions:
1. What is the density of water?
2. Why was coke’s density greater thank the
diet coke?
Agenda
• Scientific Notation Notes
• Scientific Notation Practice
Scientific Notation
Why Scientists Use Scientific Notation
• The Hope Diamond contains about
460,000,000,000,000,000,000,000 atoms of
carbon
• Each carbon atom has a mass of
0.00000000000000000000002 g
• To calculate the mass of
the Hope Diamond, you
would multiply the number
of carbon atoms by the
mass of one carbon atom
Why Scientists Use Scientific Notation
• Sounds easy enough, except for the fact that all
those zeros would get in the way!
• Using a calculator offers no help, as it won’t let
you enter numbers this large or this small
• Numbers such as these are best expressed in
scientific notation
• This method allows
scientists to restate
numbers without
changing their value
Scientific Notation
• Scientific notation can be used to express any
number as a number from 1 through 9 (known
as the coefficient) multiplied by 10 raised to a
power (known as the exponent)
• Carbon atoms in Hope Diamond = 4.6 x 1023
Coefficient
• Mass of one carbon atom = 2 x 10-23
Exponent
Scientific Notation
• In each case, the number 10 raised to an
exponent replaced the zeros that preceded or
followed the nonzero numbers
• For numbers greater than 1, a positive exponent
is used to indicate how many times the
coefficient must be multiplied by 10 in order to
obtain the original number
• For numbers less than 1, a negative exponent
indicates how many times the coefficient must be
divided by 10 in order to obtain the original
number
Scientific Notation
• Determining the exponent to use when writing a
number in scientific notation is easy!
• Simply count the number of places the decimal
point must be moved to give a coefficient from 1
through 9
• The number of places moved equals the value of
the exponent
• The exponent is positive when the decimal moves
to the left
• The exponent is negative when the decimal
moves to the right
Scientific Notation
• 460,000,000,000,000,000,000,000.  4.6 x 1023
– Because the decimal point moves 23 places to the
left, the exponent is 23
• 0.00000000000000000000002  2 x 10-23
– Because the decimal point moves 23 places to the
right, the exponent is -23
Scientific Notation Practice
• Express each number in scientific notation
– 700 = 7 x 102
– 45,000,000 = 4.5 x 107
– 0.0000000008 = 8 x 10-10
• Express each quantity in regular notation
along with its appropriate unit
– 3.60 x 105 s = 360,000 s
– 5.4 x 10-5 g/cm3 = 0.000054 g/cm3
– 5.060 x 103 km = 5060 km
Arithmetic and Scientific Notation
• This is easy when using your calculator – JUST
MAKE SURE YOU KNOW HOW TO DO IT!!
• Practice
– (3 x 104) + (5 x 10-8) = 3 x 104
– (2 x 106) - (1 x 107) = -8 x 106
– (6 x 109) x (2 x 10-3) = 1.2 x 107
– (8 x 103) ÷ (4 x 10-2) = 2 x 105
Scientific Notation Practice
DYL
1. Does a positive exponent imply a big or small
number?
2. Does a negative exponent imply a big or small
number?