Download Section 3B Putting Numbers in Perspective

Section 3B
Putting Numbers in Perspective
Pages 154-171
3-B
Scientific Notation
Absolutely critical for very large and very
small numbers
Ex1/155
The federal debt is $9,100,000,000,000.
The diameter of a hydrogen nucleus is
0.0000000000000001 meter.
Your calculators automatically use it!
3-B
Scientific Notation
Scientific Notation is a format in which a number
is expressed as a number between 1 and 10
multiplied by a power of 10.
Examples:
9,100,000,000,000 = 9.1  1012
= 9.1 E 12 (calculator)
0.0000000000000001 = 1.0  1016
= 1 E -16 (calculator)
3-B
Scientific Notation
106 = 1 million = 1,000,000
109 = 1 billion = 1,000,000,000
1012 = 1 trillion = 1,000,000,000,000
•
The U.S. federal debt is about $9.1 trillion
($9.1×1012)
3-B
Ordinary vs Scientific Notation
An exercise in powers of 10 and moving the
decimal
KEY:
X 10(positive p) moves decimal p places to right.
X 10(negative p) moves decimal p places to left.
3-B
Examples:
1.7842  103
= 1784.2
2.111  107
= 21,110,000
9.1  10-4
= .00091
Conversion from scientific to ordinary
3-B
Example:
1330
= 1.330  103
.00000345
= 3.45  10-6
527  103
= 5.27  102  103 = 5.27  105
Conversion from ordinary to scientific
3-B
Using your Calculator
Look for an “EE” key
1.7842  103
1.7842
EE
3
= 1784.2
2.111  107
2.111
EE
7
= 21110000
9.1  10-4
9.1
EE
-4
= 0.00091
1000 = 1.0 x 103
1.0
not (10)
EE
EE
3
3
More Practice
25/164 Convert from scientific to ordinary
27/164 Convert from ordinary to scientific.
33/164 Total annual energy consumption in the US is
about 100,000,000,000,000,000,000 joules.
35/164 The hard drive on my computer has a
capacity of 12.0 gigabytes (recall ‘giga’ = billion).
37/164 The diameter of a typical bacterium is about
0.000001 meter.
3-B
Multiply or Dividing with scientific notation:
Examples: 6200 x 300000
(6.2  103)× (3  105) = (6.2×3)×(103×105)
= 18.6×10(3+5)
= 1.86 ×10 x 108 = 1.86 x 109
420
4.2  102 = 4.2 × 102
.000084 8.4  10-5
8.4 10-5
= .5×102-(-5) = .5×107
= 5.×10(-1) x 107 = 5.0 x 106
More Practice 29/168
3-B
Why Scientific Notation: Approximations
Example:
14927  2213
≈ 15000 × 2000
= (1.5×104)× (2 × 103)
= 3×107
= 30,000,000 (30 million)
check: 14927  2213 = 33,033,451
More Practice: Ex2/155
8 million residents produce 1.8 lb or .0009 tons of
trash each day. Estimate the total amount of trash
produced each day. [225 tons?]
3-B
Why Scientific Notation: Calculator Issues
Total annual energy consumption in the US is about
100,000,000,000,000,000,000 joules.
Convert to kilowatt-hours.
1 kilowatt  hour
100, 000, 000, 000, 000, 000, 000 joules 
3.6million joules
11020
kilowatt  hours
6
3.6 10
= .278 x 1014 = 2.78 x 10(-1) x 1014 = 2.78 x 1013
Homework:
Pages 168
# 26 28, 34, 36, 38, 40