2. The Metric (SI) System Unit 1

3. SI = Systeme Internationale  Used in Science  Used throughout the world (except in U.S.A.) for all measurements  Based on “10s”

4. Base Units  Length = Meters (m)  Mass = Grams (g)  Volume = Liters (L)  Temperature = Kelvins or Celsius (based on absolute zero: -273ºC = 0 K) –4 ºC = refrigerator –20-22 ºC = room temperature –37 ºC = body temperature  NOTE: base units do not get a prefeix!!

5. Metric Prefixes you MUST Memorize!!!! Metric Prefixes To Memorize!!! Giga (G)10 9 Mega (M)10 6 Kilo (k)10 3 Base Units – [m, L, g]1 Centi (c)10 -2 Milli (m)10 -3 Micro (µ)10 -6 Nano (n)10 -9

6. Measurements can be:  Accurate – Close to the “true” value (with mutliple trials compare the average to the true value)  Precise – Reproducibility in replicate measurements (each measurement is close to all of the others) Neither accurate nor precise Precise but not accurate Precise AND accurate

7. Reading the Meniscus on a graduated Cylinder Always read volume from the bottom of the meniscus. The meniscus is the curved surface of a liquid in a narrow cylindrical container.

8. Try to avoid parallax errors. Parallax errors arise when a meniscus or needle is viewed from an angle rather than from straight-on at eye level. Correct: Viewing the meniscus at eye level Incorrect: viewing the meniscus from an angle

9. Significant Figures. in Measurement 1. Identify the smallest unit that your device accurately measures to. 2. Estimate one digit past that smallest unit. –Ex. If the smallest division is ones, you estimate to the 10ths. 52.8 mL Measurement?

10. Reading the Thermometer Determine the readings as shown below on Celsius thermometers:.  C 875 350

11. Your Turn: How many meters? 0.72 m 350 m

12. How many mL? 4800 mL

13. How many cm? How many mm? 7.15 cm 71.5 mm

14. 10 mL Graduate What is the volume of liquid in the graduate? (This one is tricky).. mL66

15. 25mL graduated cylinder What is the volume of liquid in the graduate?. mL115

16. Practice  WS #1 -- Sig Figs in Measurement WS #1 -- Sig Figs in Measurement  Metric Measurements Lab

17. Scientific Notation  Why is Scientific Notation important? –Make really big or really small numbers more manageable. –Helps keep track of significant figures.  In scientific notation, numbers are written as M x 10 n.  “M” must be a number between 0 and 10 (not including 0 or 10). Therefore, there must be one, and only one, number to the left of the decimal point; e.g., 2.35 x 10 5 meters.  156000 cm = 1.56 x 10 5 cm –Moving decimal left = (+) exponent –Multiplying by 10 5 = x 100,000  0.0000245 km = 2.45 x 10 -5 km –Moving decimal to right = (-) exponent –Multiply by 10 -5 = dividing by 100,000

18. Practice Convert to or from scientific notation:  1,456  0.00349  23.45  1 x 10 7  3.45 x 10 5  3.98 x 10 -3  2.34 x 10 -5 1.456 x 10 3 3.49 x 10 -3 2.345 x 10 1 10,000,000 345,000 0.00398 0.0000234

19. Practice  WS #2 Scientific Notation WS #2 Scientific Notation

20. Significant Digits (Figures) AAll non-zero digits are significant 99878 mL has 4 sig figs ZZeros appearing between non-zero digits are significant  403 L has 3 sig figs 504.07 L has 5 sig figs

21. Sig. Figs. (Cont.)  Zeros to the right of a non-zero digit and to the right of a decimal are significant  85.00 has 4 sig figs. 9.000000000 has 10 sig figs.  Zeros that appear in front of non- zero digits are not significant  0.095897 m has 5 sig figs 0.0009 Kg has 1 sig fig

22. Sig. Figs. (Cont.)  Zeros at the end of a number but to the left of a decimal may or may not be significant. If such a zero has been measured or is the first estimated digit, it is significant. If the zero has not been measured or estimated but is just a place holder, it is NOT significant.  2000 m may contain from 1 to 4 sig. figs depending on how many zeros are placeholders.  2000. definitely has 4, as indicated by the decimal.  This number can be rewritten in scientific notation to indicate any number of sig figs., e.g.:  2.0 x 10 3 has 2 sig figs

23. Sig. Figs, (Cont.)  Any counting numbers have an infinite number of significant digits.  250 cows has an infinite number of significant digits.  Conversion factors are never used to determine significant digits.  E.g., 12 inches/1ft

24. How many sig figs in:  28.6 g  3340 cm  3340. cm  0.07080 m  9.8000 L  0.0067000 Kg  20 cars 3 4 3 5 5 Infinite – counting number 4

25. Practice  WS #3 – Significant Figures WS #3 – Significant Figures

26. Adding & Subtracting Sig. Figs.  The answer must have the same number of decimal places as there are in the measurement having the fewest decimal places.  Only adjust sig figs in your final answer 50.2 g – 32 g 57.712  57.71 g 44.15  44.2 L 4.8 ºC 18.2  18 g 25.652 g + 32.06 g = ? 42.1 L + 2.05 L = ? 36.6 ºC – 31.8 ºC

27. Multiplying & Dividing Sig. Figs.  The answer can have no more significant figures than are in the measurement with the fewest number of significant figures.  REMEMBER: Conversion factors are not significant! 50.2 g / 32 g 100,366 g  1.00 x 10 5 g 21.05  21.1 L 32.1552 x 10 8 m 2  3.22 x 10 9 m 2 1.56875  1.6 g 134 g x 749 g = ? 42.1 L / 2.00 L = ? 3.60 x 10 3 m x 8.932 x 10 5 m

28. Sig Figs in Combined Calculations  In calculations that combine addition, subtraction, multiplication, & division, sig figs are followed, but not included until the final answer.  Underline your sig figs in addition and subtraction to keep track  https://www.youtube.com/watch?v=__csP0 NtlGI https://www.youtube.com/watch?v=__csP0 NtlGI

29. Combined Example

30. Practice  WS #4 – Sig Figs in Calculations WS #4 – Sig Figs in Calculations  Metric Measurement Lab

31. Percent Error Calculation  Measures how far off from the accepted (theoretical) value the experimental value is.

32. Percent Error Example: A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The actual value of the density is 1.36 g/mL. What is the percent error of this measurement? % Error = 1.36 g/mL - 1.40 g/mL X 100 1.36 g/mL = 2.94% = 3%

33. Practice  WS #5 – Percent Error Calculations  WS #6 -- #5 SciNotSigFig%Error Review