1. Section 3B Putting Numbers in Perspective
Pages

2. 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 meter.
Your calculators automatically use it!

3. 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)
= 1.0  1016
= 1 E -16 (calculator)

4. Scientific Notation 109 = 1 billion = 1,000,000,000
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)

5. Ordinary vs Scientific Notation
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.

6. Conversion from scientific to ordinary
3-B
Examples:
 103 =
2.111  107
= 21,110,000
9.1  10-4 =
Conversion from scientific to ordinary

7. Conversion from ordinary to scientific
3-B
Example:
1330
=  103
= 3.45  10-6
527  103
= 5.27  102  103 = 5.27  105
Conversion from ordinary to scientific

8. Using your Calculator Look for an “EE” key 1.7842  103
3-B
Using your Calculator
Look for an “EE” key
 103
EE =
2.111  107
EE =
9.1  10-4
9.1 EE -4 =
1000 = 1.0 x 103
1.0 EE 3
not (10) EE 3

9. 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 meter.

10. Multiply or Dividing with scientific notation:
3-B
Examples: x
(6.2  103)× (3  105) = (6.2×3)×(103×105)
= 18.6×10(3+5)
= 1.86 ×10 x 108 = 1.86 x 109
 = 4.2 × 102 
= .5×102-(-5) = .5×107
= 5.×10(-1) x = 5.0 x 106
More Practice 29/168

11. Why Scientific Notation: Approximations
3-B
Why Scientific Notation: Approximations
Example:
14927  2213
≈ × 2000
= (1.5×104)× (2 × 103)
= 3×107
= 30,000,000 (30 million)
check:  2213 = 33,033,451
More Practice: Ex2/155 8 million residents produce 1.8 lb or tons of trash each day. Estimate the total amount of trash produced each day. [225 tons?]

12. Why Scientific Notation: Calculator Issues
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.
= .278 x 1014 = x 10(-1) x 1014 = 2.78 x 1013

13. Homework:
Pages 168
# 26 28, 34, 36, 38, 40