1. Scientific Notation

2. How far away is the nearest Star besides our Sun (Proxima Centauri)?
km (13 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

3. Scientific Notation
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 (neg. and pos. whole number)

4. Write the distance to Proxima Centauri in scientific notation.
km 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 4 and the 0

5. 4.0,000,000,000,000.
How many decimal places did you move the decimal? 13 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 4.0 X 1013

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

7. Write 28750.9 in scientific notation.
x 10-5
x 10-4
x 104
x 105

8. Example 1
Given: 289,800,000
Use:
Answer: x 108

9. Example 2
Given:
Use: 5.67
Answer: 5.67 x 10-4

10. 2) Express 1.8 x 10-4 in decimal notation.

11. Write in PROPER scientific notation
Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) x 109
2.345 x 1011
9) x 104
6.42 x 102

12. Write 531.42 x 105 in scientific notation.

13. Example 3
Given: x 106
Answer: 5,093,000

14. Example 4
Given: x 10-4
Answer:

15. Significant Digits and Scientific Notation
When trying to determine the number of significant digits within scientific notation we leave it the way it is and follow the same rules and pretend the x 10n is not there.
E.g.
x10-4 has ___ significant digits
5.3x1015 has ___ significant digits