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The Metric (SI) System

The Metric (SI) System. Unit 1. SI = S ysteme I nternationale. Used in Science Used throughout the world (except in U.S.A.) for all measurements Based on “10s”. Base Units. Length = Meters (m) Mass = Grams (g) Volume = Liters (L)

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The Metric (SI) System

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  1. The Metric (SI) System Unit 1

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

  3. 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

  4. Metric Prefixes you MUST Memorize!!!!

  5. 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) Precise but not accurate Precise AND accurate Neither accurate nor precise

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

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

  8. Identify the smallest unit that your device accurately measures to. Estimate one digit past that smallest unit. If the smallest division is ones, you estimate to the 10ths. Sig. Figs. in Measurement

  9. Use the graduations to find all certain digits There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are… • Lab techniques lab 52 mL.

  10. Estimate the uncertain digit and take a reading The meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is _______. 0.8 mL The volume in the graduated cylinder is 52.8 mL.

  11. 10 mL Graduate What is the volume of liquid in the graduate? (This one is tricky). 6 . mL 6

  12. 25mL graduated cylinder What is the volume of liquid in the graduate? . mL 1 1 5

  13. Reading the Thermometer Determine the readings as shown below on Celsius thermometers: 3 5 0 . C 8 7 5 . C

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

  15. How many mL? 4800 mL

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

  17. Practice • WS #1 -- Sig Figs in Measurement • Lab Techniques Lab

  18. 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 10n. • “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 105 meters. • 156000 cm = 1.56 x 105 cm • Moving decimal left = (+) exponent • Multiplying by 105 = 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

  19. Practice Convert to or from scientific notation: • 1,456 • 0.00349 • 23.45 • 1 x 107 • 3.45 x 105 • 3.98 x 10-3 • 2.34 x 10-5 1.456 x 103 3.49 x 10-3 2.345 x 101 10,000,000 345,000 0.00398 0.0000234

  20. Practice • WS #2 Scientific Notation

  21. All non-zero digits are significant 9878 mL has 4 sig figs Significant Digits (Figures) • 403 L has 3 sig figs 504.07 L has 5 sig figs • Zeros appearing between non-zero digits are significant

  22. 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. Sig. Figs. (Cont.) • 0.095897 m has 5 sig figs 0.0009 Kg has 1 sig fig • Zeros that appear in front of non-zero digits are not significant

  23. 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 103 has 2 sig figs

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

  25. 28.6 g 3340 cm 3340. cm 0.07080 m 9.8000 L 0.0067000 Kg 20 cars How many sig figs in: 3 3 4 4 5 5 Infinite – counting number

  26. Practice • WS #3 – Significant Figures

  27. 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 Adding & Subtracting Sig. Figs. 25.652 g + 32.06 g = ? 57.712 57.71 g 42.1 L + 2.05 L = ? 44.15  44.2 L 36.6 ºC – 31.8 ºC 4.8ºC 18.2  18 g

  28. 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 Multiplying & Dividing Sig. Figs. 42.1 L / 2.00 L = ? 21.05  21.1 L 134 g x 749 g = ? 100,366 g  1.00 x 105 g 3.60 x 103 m x 8.932 x 105 m 32.1552 x 108 m2 3.22 x 109 m2 1.56875  1.6 g

  29. 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=__csP0NtlGI

  30. Combined Example

  31. Practice • WS #4 – Sig Figs in Calculations • Metric Measurement Lab

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

  33. 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%

  34. Practice • WS #5 – Percent Error Calculations • Don’t forget significant figures!!!

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