1. Homework
Questions?

2. Scientific Notation Good to represent very big or very small numbers
Used often in math and sciences
Scientific notation is written as a x 10n where ___ ≤ a < ____ and n is an integer.

3. Converting
We should remember how to convert between standard notation and scientific notation from science class.
For example:
2,340,000 is in standard form
2.34 x 106 is in scientific notation
3.21 x 10-9 is in scientific notation
is in standard form

4. Converting
To convert from standard to scientific, move the decimal until you get a number between 1 and 10. The number of places is your exponent.
To convert from scientific to standard, move the decimal as many places as the power of ten.
Positive exponents give us ______ numbers
Negative exponents give us ______ numbers

5. Convert Convert to Scientific Notation Convert to Standard Notation
820,000,000
602,000,000,000,000,000
.02103 8
4.5 x 107
8.01 x 10-4
1.762 x 102
3 x 10-1
9.99 x 1010

6. Operations with Scientific Notation
Adding and Subtracting
Remember: the power of ten is the most significant part!
What is (4 x 103) + (5 x 105)? Not 9 x 108…

7. Simplify. Answers should be in scientific notation.
(2 x 105) + (6 x 103)
(8 x 10-4) + (3 x 10-5)
(9 x 104) - (2 x 106)

8. Operations with Scientific Notation
Multiplying
Remember how to multiply powers
What is (2 x 103) x (4 x 105)?

9. Operations with Scientific Notation
Dividing
Remember how to divide powers
What is (8 x 103) ÷ (5 x 105)?

10. Simplify. Answers should be in scientific notation.
(2.5 x 10-4) x (3 x 106)
(3 x 106) ÷ (3 x 109)
(9 x 104) x (2 x 106)

11. Adjusting scientific notation answers
Sometimes our answer won’t be in scientific notation when we find them. The a value may be too big or too small.
If a is too big, then the number is bigger than we thought. Bigger numbers have (+) exponents. We should add 1 to the exponent and move the decimal point back one place.
If a is too small, then the number is smaller than we thought. Smaller numbers have (–) exponents. We should subtract 1 from the exponent and move the decimal point forward one place.

12. In short…
If you were multiplying and need to adjust, move the decimal and ADD one to the new exponent.
If you were dividing and need to adjust, move the decimal and SUBTRACT one from the new exponent.

13. Simplify. Answers should be in scientific notation.
(7 x 10-3) x (6 x 104)
(1.2 x 1012) ÷ (4 x 10-7)
(4.8 x 10-5) ÷ (6 x 106)

14. Homework
Multiplying/Dividing Scientific Notation

15. Uses
A snail crawls at about 5 x 10-3 miles per hour. If it crawls for a year (about 8.7 x 103 hours), how far would the snail crawl?
Distance = Rate x Time

16. Uses
A computer pixel has an area of about 9 x 10-9 sq. m. A movie theater screen is about 7.5 x 102 sq. m. How many pixels would we need to create a movie theater sized computer screen?

17. Comparisons
A virus weighs 2 x kg and a blue whale weighs 3 x 105 kg.  How many viruses would we need to outweigh a blue whale?
If there are 1 x 1031 viruses on the planet and about 1.2 x 104 blue whales, which one contributes more mass to the planet?  How much more mass?

18. Biomass refers to the total amount of living material in a system
Biomass refers to the total amount of living material in a system. For example, you could refer to the biomass of humanity as the mass of all the humans in the world together.
The average human weighs about 200 lbs. There are about 9,000,000,000 humans. What is the biomass of humanity?

19. Comparisons
A human weighs about 200 lbs. There are about 9,000,000,000 humans.
An ant weighs about lbs. There are about 1,000,000,000,000,000,000 ants.
A blue whale weighs about 400,000 lbs. There are about 10,000 blue whales.
Which has more biomass?

20. Comparisons Ants: 5 x 1013 lbs Humans: 1.8 x 1012 lbs
Whales: 4 x 109 lbs
By mass, how many times more ants are there than blue whales?
By mass, how many times more ants are there than humans?

21. Conclusion?
If it came down to a fight between humans and ants, who wins?

22. Multiply or Divide?
A notebook page has 100 lines. My notebook has 200 pages. How many lines are in my notebook?
A penny weighs about .002 lbs. An average elephant weighs about 4000 lbs. How many pennies would weigh as much as an elephant?
A dollar bill is .003 m thick. The sun is about 144,000,000,000 m away from earth. How many dollar bills would you stack to reach the sun?
A dollar bill is .003 m thick. The national debt is about $18,000,000,000,000. How far would a stack of this many dollar bills reach?