Understanding Scientific Notation: Powers of Ten

1. Powers of Ten / Scale Mr. Davis

2. Why do we care? • Cannot describe many things in science apart from powers of 10 • Scientific notation useful in Physics, Chemistry, Economics, Programming, Engineering, …

3. http://powersof10.com/film

4. Scientific Notation By Jenny Erickson

5. What is scientific Notation? • Scientific notation is a way of expressing really big numbers or really small numbers. • It is most often used in “scientific” calculations where the analysis must be very precise.

6. Why use scientific notation? • For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. • Numbers expressed in scientific notation can be used in a computation with far greater ease.

7. Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 N x 10x

8. Which of these are in scientific notation? What are the common equivalents? 1.0 X 100 10.2 X 102 0.1 100 1.5 x 101

9. Changing standard form to scientific notation.

10. To change standard form to scientific notation… • Place the decimal point so that there is one non-zero digit to the left of the decimal point. • Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

11. Continued… • If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

12. Example 1 • Given: 289,800,000 • Use: 2.898 (moved 8 places) • Answer: 2.898 x 108

13. Example 2 • Given: 0.000567 • Use: 5.67 (moved 4 places) • Answer: 5.67 x 10-4

14. Changing scientific notation to standard form.

15. To change scientific notation to standard form… • Simply move the decimal point to the right for positive exponent 10. • Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

16. Example 3 • Given: 5.093 x 106 • Answer: 5,093,000 (moved 6 places to the right)

17. Example 4 • Given: 1.976 x 10-4 • Answer: 0.0001976 (moved 4 places to the left)

18. How do I convert these to scientific notation? 0.123456789 123456789 1,000,000,000,000,000,000 0.000000000123456789 ( 0.000 000 000 123456789)

19. Multiplying and Dividing

20. Multiplying in Scientific Notation

21. Multiplying… • The general format for multiplying is as follows… • (N x 10x)(M x 10y) = (N)(M) x 10x+y • First multiply the N and M numbers together and express an answer. • Secondly multiply the exponential parts together by adding the exponents together. • Finally multiply the two results for the final answer.

22. Multiplying… • (2.41 x 104)(3.09 x 102) • 2.41 x 3.09 = 7.45 • 4 + 2 = 6 • 7.45 x 106

23. Dividing in Scientific Notation

24. Dividing… • The general format for dividing is as follows… • (N x 10x)/(M x 10y) = (N/M) x 10x-y • First divide the N number by the M number and express as an answer. • Secondly divide the exponential parts by subtracting the exponent from the exponent in the upper number. • Finally multiply the two results together to get the final answer.

25. Dividing… • (4.89 x 107)/(2.74 x 104) • 4.89 / 2.74 = 1.78 • 7 – 4 = 3 • 1.78 x 103

26. Even More Practice • Below is a list of links to games and activities all having to do with scientific notation. • http://www.aaamath.com/dec71i-dec2sci.html • http://janus.astro.umd.edu/cgi-bin/astro/scinote.pl • http://www.sciencejoywagon.com/physicszone/lesson/00genral/dectosci.htm

27. Now take the quiz to test your scientific notation skills! • Click on the link below to take the quiz and then use the answer key for the correct answers. • Quiz • Answers

28. Quiz Time!!! • Below is a set of links for a quiz on multiplying and dividing numbers in scientific notation, and there is a link to get the answers to the quiz. • Quiz on Multiplying and Dividing • Answers to Quiz