Tuesday 9/16/14
Learning Target:
Know how to use and convert
numbers into scientific notation.
Learning Outcome:
I will be able to use scientific
notation in problems and convert
standard notation into scientific
notation.
Chapter 1
1
Why are significant figures
not important in your math
class?
Chapter 1
2
Perform the following calculations to the
correct number of significant figures
a)
1 . 10  0 . 5120  4 . 0015  3 . 4555 
b) 0.355 + 105.1 - 100.5820 =
c)
4 . 562  3 . 99870   452 . 6755  452 . 33  
d)
14 . 84  0 . 55   8 . 02

Perform the following calculations to the
correct number of significant figures
a)
1 . 10  0 . 5120  4 . 0015  3 . 4555  0 . 652
b) 0.355 + 105.1 - 100.5820 = 4.8739 = 4.9
c)
d)
4 . 562  3 . 99870   452 . 6755  452 . 33   52 . 799  52 . 80
14 . 84  0 . 55   8 . 02
 0 . 142  0 . 14
What is scientific notation?
 A method used in science to
represent really large of really small
numbers.
 Used to show significant figures with
ambiguous numbers (large numbers
without decimal points)
Numbers in Chemistry
 Avogadro’s Number

602,000,000,000,000,000,000,000 atoms/mol
 Planck's Number

0.000000000000000000000000000000000662 J/s
 Speed of Light
 300,000,000 m/s
 Wavelength of red light
 .000000750 m
Positive Exponents




101
102
103
104
=
=
=
=
10
10X10= 100
10X10X10 = 1000
10X10X10X10 = 10,000
Negative Exponents




10-1
10-2
10-3
10-4
=
=
=
=
1/10 = 0.1
1/100 = 0.01
1/1000 = 0.001
1/10000 = 0.0001
Scientific Notation
 10,000 = 1 X 104
 250,000 = 2.5 X 105
 Count places to the left until there is one number to
the left of the decimal point.
 230,000 = ?
 35,000 = ?
Scientific Notation Continued
 0.00006 = 6 X 10-5
 0.00045 = 4.5 X 10-4
 Count places to the right until there is one
number to the left of the decimal point
 0.003 = ?
 0.0030 = ?
 0.0000025 = ?
Convert the following numbers into
scientific notation
 45.01
 0.00671
 5,712,100
Convert the following numbers into
scientific notation
 45.01 = 4.501 x 101
 0.00671 = 6.71 x 10-3
 5,712,100 = 5.7121 x 106
Convert the following numbers into
standard notation:




9.11 x 103
1.75 x 107
7.4 x 10-5
9 x 10-4
Convert the following numbers into
standard notation:




9.11 x 103 = 9110
1.75 x 107 = 17,500,000
7.4 x 10-5 = 0.000074
9 x 10-4 = 0.0009
Multiplying with Scientific Notation
 Add the Exponents
 102 X 103 = 105
 100 X 1000 = 100,000
Multiplying with Scientific Notation
(2.3 X 102)(3.3 X 103)

Multiply the Coefficients

2.3 X 3.3 = 7.59 = 7.6

Add the Exponents

102 X 103 = 105

Put them together, 7.6 X 105

760,000
Multiplying with Scientific Notation
 (4.6 X 104) X (5.5 X 103) = ?
 (3.1 X 103) X (4.2 X 105) = ?
 (6.72 x 105) x (7.33 x 10-9)= ?
Multiplying with Scientific Notation
 (4.6 X 104) X (5.5 X 103) = 2.5 x 108
 (3.1 X 103) X (4.2 X 105) = 1.3 x 109
 (6.72 x 105) x (7.33 x 10-9)= 4.93 x 10-3
Dividing with Scientific Notation
 Subtract the Exponents
 104/103 = 101
Dividing with Scientific Notation

(3.3 X 104)/ (2.3 X 102)

Divide the Coefficients

3.3/ 2.3 = 1.434783 = 1.4

Subtract the Exponents

104 / 102 = 102

1.4 X 102

140
Dividing with Scientific Notation
 (4.6 X 106) ÷ (5.5 X 103) =
 (3.1 X 108) ÷ (4.262 X 104) =
 (6.72 x 105) ÷ (7.3 x 10-9)=
Dividing with Scientific Notation
 (4.6 X 106) ÷ (5.5 X 103) = 8.4 x 102
 (3.1 X 108) ÷ (4.262 X 104) =
7.3 x 103
 (6.72 x 105) ÷ (7.3 x 10-9)=
9.2 x 1013