PowerPoint The First

1. PowerPoint The First In which you will find information on: the metric (SI) system of measurement uncertainty in measurements how to count sig figs

2. Units of Measurement In every measurement there is a • Numberfollowed by a • Unit from a measuring device • Numbers without a unit are naked numbers (NN)!

3. Some Tools for Measurement Which tool(s) would you use to measure: A. temperature B. volume C. time D. weight

4. Standards of Measurement When we measure, we use a measuring tool to compare some dimension of an object to a standard. For example, at one time the standard for length was the king’s foot. What are some problems with this standard?

5. What do we use in science? • The metric system – based on units of 10 • Specifically, we use the SI system which has specific standards for 7 basic units

6. SI measurement • Le Système international d'unités • The only countries that have not officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularly • Metrication is a process that does not happen all at once, but is rather a process that happens over time. • Among countries with non-metric usage, the U.S. is the only country significantly holding out. The U.S. officially adopted SI in 1866. Information from U.S. Metric Association

7. UNITS OF MEASUREMENT Use SI units — based on the metric system Length Mass Volume Time Temperature Meter, m Kilogram, kg Liter, L Seconds, s Celsius degrees, ˚C kelvins, K

8. Didn’t I say there were SEVEN base units? Find the new ones!

9. What’s the most important measurement to chemists? • The mole! • A mole is a measure of the # of particles in a substance. • Analogy – 1 dozen eggs: 12 eggs as 1 mole atoms : 6.022 x 1023 atoms

10. Metric Prefixes • Used for convenience – wouldn’t want to describe the mass of a penny in kilograms! • Kilo- means 1000 of that unit • 1 kilometer (km) = 1000 meters (m) • Centi- means 1/100 of that unit • 1 meter (m) = 100 centimeters (cm) • 1 dollar = 100 cents • Milli- means 1/1000 of that unit • 1 Liter (L) = 1000 milliliters (mL)

11. Metric Prefixes

12. Metric Prefixes

13. O—H distance = 9.4 x 10-11 m 9.4 x 10-9 cm 0.094 nm Units of Length • ? kilometer (km) = 500 meters (m) • 2.5 meter (m) = ? centimeters (cm) • 1 centimeter (cm) = ? millimeter (mm) • 1 nanometer (nm) = 1.0 x 10-9 meter

14. Volume = length x length x length

15. Chemistry In Action On 9/23/99, $125,000,000 Mars Climate Orbiter entered Mars’ atmosphere 100 km lower than planned and was destroyed by heat. 1 lb = 1 N 1 lb = 4.45 N “This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”

16. Uncertainty in Measurement • When making measurements, one must always estimate an extra decimal place (if it is a non-digital display) • This extra place is uncertain

17. How many decimal places can you read on each of these?

18. Significant Figures • The numbers reported in a measurement are limited by the measuring tool • Significant figures in a measurement include the known digits plus one estimated (uncertain) digit

19. Significant Figures and Calculations • Measurements in the lab must be made accurately! • But what does that mean?

20. Reading a Meterstick . l2. . . . I . . . . I3 . . . .I . . . . I4. . cm First digit (known) = 2 2.?? cm Second digit (known) = 0.7 2.7? cm Third digit (estimated) between 0.05- 0.07 Length reported =2.75 cm or 2.74 cm or 2.76 cm

21. Known + Estimated Digits In 2.76 cm… • Known digits 2 and 7 are 100% certain • The third digit 6 is estimated (uncertain) • In the reported length, all three digits (2.76 cm) are significant including the estimated one

22. Zero as a Measured Number . l3. . . . I . . . . I4 . . . . I . . . . I5. . cm What is the length of the line? First digit 5.?? cm Second digit 5.0? cm Last (estimated) digit is5.00 cm

23. ALWAYS estimate ONE place past the smallest mark! 11.51

24. What happens when measurements are used in calculations? • Measurements are only as good as the instruments used to make them! • Imagine calculating the volume of a cube with three different rulers: 2.4 cm x 2.45 cm x 2.453 cm = 14.42364 cm3 • The answer has way too many digits! None of the rulers were able to measure all 5 decimal places! • Instead, we use significant figures to show the accuracy of a measurement.

25. 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 3 5

26. Leading Zeros RULE 2. Leading zeros in decimal numbers are NOTsignificant. Number of Significant Figures 0.008 mm 1 0.0156 oz 3 0.0042 lb 0.000262 mL ____ 2 3

27. 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 min 4 0.702 lb 0.00405 m ____ 3 3

28. Trailing Zeros RULE 4. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders. Number of Significant Figures 25,000 in. 2 200. yr3 48,600 gal 25,005,000 g 3 5

29. HOMEWORK EXERCISES • These questions are due the next time our class meets. • For each of the following pieces of glassware, provide a sample measurement and discuss the number of significant figures and uncertainty. CONTINUED…

30. HOMEWORK CONT’D 2) Which of the following are exact numbers? a. The elevation of Breckenridge, CO is 9600 ft. b. There are 12 eggs in a dozen. 3) How many sig figs are in each of the following? a. 12 b. 1098 c. 2.001 x 103 d. 0.0000101 4) Round each number to 3 sig figs. a. 312.54 b. 0.00031254 c. 31, 254, 000