1. Scientific Notation and Significant Figures

2. Why do we use Scientific Notation?

3. Why do we use Scientific Notation? Chemists often use very LARGE and very SMALL numbers Examples: Mass of H atom: 0.000 000 000 000 000 000 000 001 67 g Mole of atoms: 602 000 000 000 000 000 000 000

4. Scientific Notation • Written as a COEFFICIENT and a POWER OF 10 • Example 1: 2300 = 2.3 x 103 Number of times coefficient must be multiplied by ten to get original number Coefficient ≥ 1 AND <10

5. Example 2: 0.0052 =

6. Example 2: 0.0052 = 5.2 x 10-3

7. Convert to Scientific Notation

8. Convert to Scientific Notation

9. Convert to Standard Form

10. Convert to Standard Form

11. Significant Figures • Scientists report measurements using significant figures • SF: a measurement that includes all the precisely known digits plus a last digit that must be estimated

12. Measuring using Sig Figs

13. What is the length of each object?

14. Sig Fig Rules • Every nonzero digit is significant • Zeros between nonzero digits are significant • Zeros in front of all nonzero digits are NOT significant • Zeros at the end of a number and to the right of a decimal are significant • Zeros at the end of a measurement and to the left are NOT significant if there is no decimal at the end

15. How many Sig Figs? • 123 m e. 4.5600 m • 0.123 m f. 0.078 m c. 40506 m g. 0.070 80 m d. 9.8000 x 104 h. 98 000 m

16. How many Sig Figs? • 123 m (3) e. 4.5600 m (5) • 0.123 m (3) f. 0.078 m (2) c. 40506 m (5) g. 0.070 80 m (4) d. 9.8000 x 104 (5) h. 98 000 m (2)

17. Addition and Subtraction The answer can have no more digits to the right of the decimal point than the measurement with the least number of digits after the decimal. • ex. 1 12.52 + 349.0 + 8.24 = • ex. 2 740626 - 86.34 =

18. Multiplication and Division The answer must contain no more significant figures that the measurement with the least number of significant figure a. 7.44 m x 0.34 m = b. 2.4526 m / 8.4 =

19. Practice Problems Page 840, #1 Page 841, #1, 2