1. Scientific Notation Often used to express very large or very small numbers. Also used to maintain correct number of significant figures.

2. Form:(# from 1 to 9.999) x 10 exponent 800= 8 x 10 x 10 = 8 x 10 2 2531= 2.531 x 10 x 10 x 10 = 2.531 x 10 3 0.0014 = 1.4 / 10 / 10 / 10 = 1.4 x 10 -3

3. Change to standard form. 1.87 x 10 –5 = 3.7 x 10 8 = 7.88 x 10 1 = 2.164 x 10 –2 = 370 000 000 0.0000187 78.8 0.02164 000000187000000..

4. Change to scientific notation. 12 340 = 0.369 = 0.008 = 1 000 000 000 = 1.234 x 10 4 3.69 x 10 –1 8 x 10 –3 1 x 10 9

5. Using the Exponent Key on a Calculator EXPEE

6. EE or EXP means “times 10 to the…” How to type out 6.02 x 10 23 : 6EE. 0322 6y x. 0322 x 16. 02EE320y x 32 x 16. 020 Don’t do it like this… …or like this… …or like this: How to type out 6.02 x 10 23 : 6EE. 0322 WRONG! TOO MUCH WORK.

7. Also, know when to hit your (–) sign… …before the number, …after the number, …or either one.

8. Example: 1.2 x 10 5 2.8 x 10 13 But instead is written… = 1. 2EE5 32. 8 1 Type this calculation in like this: This is NOT written…4.3 –9 4.2857143 –09 Calculator gives… 4.2857143 E–09 or… 4.3 x 10 –9

9. = -6.525 x 10 -9 = 5.3505 x 10 3 or 5350.5 = 5.84178499 x 10 -13 = 2.904 x 10 23 = -3.07122 x 10 16

10. Rule for Multiplication Calculating with Numbers Written in Scientific Notation When multiplying numbers in scientific notation, multiply the first factors and add the exponents. Sample Problem: Multiply 3.2 x 10 -7 by 2.1 x 10 5 (3.2) x (2.1) = 6.72 (-7) + (5) = -2 or 10 -2 6.72 x 10 -2 Exercise: Multiply 14.6 x 10 7 by 1.5 x 10 4 2.19 x 10 12

11. Rule for Division Calculating with Numbers Written in Scientific Notation When dividing numbers in scientific notation, divide the first factor in the numerator by the first factor in the denominator. Then subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide 6.4 x 10 6 by 1.7 x 10 2 (6.4) (1.7) = 3.76 (6) - (2) = 4 or 10 4 3.76 x 10 4 Exercise: Divide 2.4 x 10 -7 by 3.1 x 10 14 7.74 x 10 -22..

12. Rule for Addition and Subtraction Calculating with Numbers Written in Scientific Notation In order to add or subtract numbers written in scientific notation, you must express them with the same power of 10. Sample Problem: Add 5.8 x 10 3 and 2.16 x 10 4 (5.8 x 10 3 ) + (21.6 x 10 3 ) =27.4 x 10 3 Exercise: Add 8.32 x 10 -7 and 1.2 x 10 -5 1.28 x 10 -5 2.74 x 10 4

13. End Sci Notation start Sig fig

14. Using Scientific Notation for Expressing the Correct Number of Significant Figures Measurement Number of significant figures it contains Measurement Number of significant figures it contains 25 g 0.030 kg 1.240560 x 10 6 mg 6 x 10 4 sec 246.31 g 20.06 cm 1.050 m 0.12 kg 1240560. cm 6000000 kg 6.00 x 10 6 kg 409 cm 29.200 cm 0.02500 g 2 2 7 1 5 4 4 2 7 1 3 3 5 4