2. Welcome to the World of Chemistry Measurement, Scientific Notation, Significant Figures

3. Numbers in Science Chemists deal with very large numbers… 602000000000000000000000 (Do you recognize this number?)

4. Count the Zeros… 299800000 m/s 0.000000000000000000000001673 That isn’t much fun! There must be a better way!?! 5 ZEROS 24 ZEROS

5. Scientific Notation  There is a way!!! HURRAY!!!  S.N. is a way of making these numbers easier to write.

6. To write these numbers in scientific notation, move the decimal so that it is expressed as:  A number between 1 and 10  Times ten to a power

7. Practice problems  12300=  2.5 X 10 3 =  1.0 X 10 -6 =  2.05 X 10 -3 =

8. Calculations  (4 X 10 2 )(2X 10 3 )=  (4X10 2 )/(2X 10 -4 )= 8 x 10 5 2 x 10 6

9. Do you and your calculator have a communication problem?  Solve the problem below using your calculator. 3.0 x 10 5 = 1.5 x 10 2 * 2.0 x 10 3

10. The Importance of Units  Numbers are used in science for quantifying measurements.  However, all numbers must be followed by a unit!!  Naked numbers have no meaning in science! Thus will never receive full credit!

11. Measurements in Science  Observations in science should be quantified whenever possible. For this reason, scientists (you) must master the tools used for measuring and the units that are used to express them.

12. General rules for measurement  All units will be metric. Memorize the units for: Length = meter (m) Length = meter (m) mass = gram (g) mass = gram (g) volume = liter (L) volume = liter (L)

13. Prefixes used with the basic units  Kilo- 1000 or 10 3  Centi- 1/100 th or 10 -2  Milli- 1/1000 th or 10 -3

14. Practice 1 kg = g1 m = cm 1 km = m1 L = mL 1 cm = m1 cm = mm 1 mL = L

15. Three targets with three arrows each to shoot. Can you hit the bull's-eye? Both accurate and precise Precise but not accurate Neither accurate nor precise How do they compare? Can you define accuracy and precision?

16. Significant Figures The numbers reported in a measurement are limited by the measuring tool The numbers reported in a measurement are limited by the measuring tool Significant figures in a measurement include the known digits plus one estimated digit Significant figures in a measurement include the known digits plus one estimated digit

17. Significant Figures (Digits)  Pay attention to the precision of your tools  Record all of the numbers in a measurement that you are certain of, plus one more (an approximation) called “the uncertainty.”  All of the measured numbers, plus the uncertain number are called significant figures.

18. Why are they important? 1.They communicate the precision of the measuring tools used by the chemist. 2.They determine how precise the answers to calculations (using the measuring tools) can be.

19. Counting Significant Figures RULE 1. All non-zero digits in a measured number are significant. Only a zero could indicate that rounding occurred. Number of Significant Figures 38.15 cm4 5.6 ft2 65.6 lb___ 122.55 m___

20. Leading Zeros RULE 2. Leading zeros in decimal numbers are NOT significant. Number of Significant Figures 0.008 mm1 0.0156 oz3 0.0042 lb____ 0.000262 mL ____

21. Sandwiched Zeros RULE 3. Zeros between nonzero numbers are significant. (They can not be rounded unless they are on an end of a number.) Number of Significant Figures 50.8 mm3 2001 min4 0.702 lb____ 0.00405 m ____

22. Trailing Zeros RULE 4. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders. Number of Significant Figures Number of Significant Figures 25,000 in. 2 25,000 in. 2 200. yr3 200. yr3 48,600 gal____ 48,600 gal____ 25,005,000 g ____

23. Practice! Determine how many significant figures each has identify which rules tell you this. 25.2 cm = 35.0 s = 0.0044 kg = 30200 m = 2.5 x 10 12 mL =

24. Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 26.54 answer 26.5 one decimal place

25. Learning Check In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.83) 257 B. 58.925 - 18.2= 1) 40.725 2) 40.733) 40.7

26. Multiplying and Dividing Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

27. Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.32) 11 3) 0.041