1. Section 8.3: Scientific Notation
Objective The student will be able to:
Express numbers in scientific and decimal notation

2. How wide is our universe?
210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

3. Who uses this?
Astronomers often work with very large numbers such as the masses of planets. The mass of each planet in the solar system is given on the next slide. Notice each value is written as the product of a number and a power of 10. These values are written in scientific notation.

4. Scientific Notation in Astronomy
Mercury 3.30x10^23
Venus 4.87x10^24
Earth 5.97x10^24
Mars 6.42X10^23
Jupiter 1.90x10^27
Saturn 5.69x10^26
Uranus 8.68x10^25
Neptune 1.02x10^26
Pluto 1.27x10^22

5. A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer

6. Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

7. 2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 1023

8. Positive Exponents (large #’s)
Example 1: 2.45 x 108 Example 2: 2.19 x 105 Example 3: 30,500,000 Example 4: 3,022,000,000,000

9. Ex. 5) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative x 10-8

10. Negative Exponents (small #’s)
Example 6: 3 x 10-5
Example 7: x 10-3
Example 8:
Example 9:

11. 10) You Try: Write 28750.9 in scientific notation.
A x 10-5 B x 10-4 C x 104 D x 105

12. You Try a few… A) 2 x 10-8 B) 4.59 x 103 C) 7.183 x 1014 D) 3.6 x 10-5G)

13. Review Positive Exponents = LARGE numbers
Move the decimals to the RIGHT
Negative Exponents = SMALL numbers
Move the decimals to the LEFT

14. 11) Express 1.8 x 10-4 in decimal notation.
) Express 4.58 x 106 in decimal notation. 4,580,000 On the graphing calculator, scientific notation is done with the button x 106 is typed

15. You Try:
Find YOUR textbook and complete the following: page 402 #16-44 Odd, 46-53
Turn in for a CW grade. Please ask the neighbor for assistance.

16. Warm-Up, Write the following in scientific notation
x 10 3

17. Answer Key
x 108
x 10-4
x 105

18. There is more to sci. notation
Numbers in scientific notation can be multiplied or divided. First multiply the decimals, then apply the product of powers or quotient of powers property to simplify the powers of 10. Next, rewrite the decimal in scientific notation and simplify the powers.. Let’ see….

19. Example 1: Use a calculator to evaluate: 4.5 x 10-5 1.6 x 10-2
You must include parentheses
(4.5 x ) (1.6 x )
Write in scientific notation.
x 10-3

20. Ex. 2: Use a calculator to evaluate:. 7. 2 x 10-9. 1
Ex. 2: Use a calculator to evaluate: x x 102 On the calculator, the answer is:
6.E -11, E = exponent!!! The answer in scientific notation is 6 x The answer in decimal notation is

21. Ex. 3: Use a calculator to evaluate (0. 0042)(330,000)
Ex. 3: Use a calculator to evaluate (0.0042)(330,000). On the calculator, the answer is
1386. The answer in decimal notation is 1386 The answer in scientific notation is x 103

22. Ex. 4: Use a calculator to evaluate (3,600,000,000)(23)
Ex. 4: Use a calculator to evaluate (3,600,000,000)(23). On the calculator, the answer is:
8.28 E +10, E = exponent The answer in scientific notation is 8.28 x The answer in decimal notation is 82,800,000,000

23. Ex. 5: Write (2.8 x 103)(5.1 x 10-7) in scientific notation.
A x 10-4 B x 10-3 C x 1010 D x 1011

24. You Try, write in scientific and standard notation
(5.3 x 102)(4.1 x 105)
(2 x 10-5)(9.4 x 10-3)
1.5 x x 1012
1.25 x x 10-6

25. You practice
Find your textbook and practice page 429 # Turn in for a CW grade.
I should hear you talking and communicating with each other!

26. Write in PROPER scientific notation
Write in PROPER scientific notation. (Notice the number is not between 1 and 10) Example 6) x 109
2.346 x 1011
Example 7) x 104
on calculator: 642
6.42 x 10 2

27. Ex. 9: Write 531.42 x 105 in scientific notation.