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Measurements

Dive into the specifics of measurements scientifically with a focus on the SI system and convert between different units effortlessly. Learn the significance of standards in measurement and unravel the mysteries of metric prefixes for precise calculations.

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Measurements

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  1. Measurements How to do it scientifically!

  2. 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 • 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

  3. 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.”

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

  6. Metric Prefixes

  7. Converting Metric • Easy way is to use a stair step method. • Units go in order from largest to smallest. • Count how many places to move the decimal based on prefixes. • LOOK AT THE BOARD. • King Henry Drinks Ultra Dark Chocolate Milk • Keep hitting Dad Until Dad Can’t Move • Kids Hate Doing Usual Decimal Counting Math • Kids Hate Doughnuts? Unusual! Doughnuts Create Mouthwater

  8. Metric Prefixes

  9. Learning Check 1. 1000 m = 1 ___ a) mm b) km c) dm 2. 0.001 g = 1 ___ a) mg b) kg c) dg 3. 0.1 L = 1 ___ a) mL b) cL c) dL 4. 0.01 m = 1 ___ a) mm b) cm c) dm

  10. Converting Standard to Metric

  11. Factor label method • The diagram below shows how all factor-label problems will be "set up" in this class. The horizontal line represents "divide by", vertical lines represent "multiply by". What is given A fraction Equal to one • Always begin your problem by writing down what is given in the problem, then drawing the horizontal and vertical lines. Another vertical line is drawn each time a different conversion factor is used.

  12. Factor Label Method • Step 1.   Show what you are given on the left, and what units you want on the right. • Step 2.   Insert the required conversion factors to change between units. • Step 3.   Continue until you get the unit you want • Step 4. Cancel units where you can, and solve the math.

  13. Simple Conversion Using FLM • The tallest living tree is the Mendocino tree at 367.5 feet tall. How many yards would this be?

  14. The tallest living tree is the Mendocino tree at 367.5 feet tall. How many yards would this be? • Step 1.   Show what you are given on the left, and what units you want on the right. • 367.5 feet = ?yards

  15. The tallest living tree is the Mendocino tree at 367.5 feet tall. How many yards would this be? • Step 2.   Insert the required conversion factors to change between units. 3 ft = 1 yard 367.5 feet 1 yard • 1 3 feet

  16. FLM • Step 3.   Cancel units where you can, and solve the math. • 367.5 feet 1 yard =367.5 = 122.5 yds 1 3 feet 3

  17. Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

  18. How many minutes are in 2.5 hours? Conversion factor 2.5 hr x 60 min = 150 min 1 hr cancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

  19. You Try This One! If Toriey stands on Niki’s shoulders, they are two and a half yards high. How many feet is that?

  20. English and Metric Conversions • If you know ONE conversion for each type of measurement, you can convert anything! • You must memorize and use these conversions: • Mass: 1 lbs = 2.2 kg • Length: 2.54 cm = 1 inch • Volume: 1.06 quarts = 1 L

  21. Learning Check An adult human has 4.65 L of blood. How many gallons of blood is that?

  22. Dealing with Two Units – If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet?

  23. How to Measure Accurately

  24. Linear measurements are made using a Meter Stick or Metric Ruler. Metric Ruler Meter Stick

  25. Estimating the last digit in a measurement You might estimate the end of the cylinder to be half-way between the lines or 0.05 cm. This digit must be included in the measurement.

  26. Estimating the last digit in a measurement This measurement should be read as 4.95 cm. This measurement has 3 significant figures.

  27. Reading a metric ruler correctly: This point can be read as 1.65 cm. or 16.5 mm.

  28. Reading a metric ruler correctly: This point can be read as 6.70 cm. or 67.0 mm.

  29. Volume Graduated Cylinders

  30. Always estimate ONE place past the smallest mark! Meniscus

  31. Temperature Thermometer

  32. Mass Triple Beam and Electronic Balance

  33. The triple beam balance:

  34. As with all measuring instruments, Sig. Fig. Rules must be followed when reading a balance. How would you read this measurement?

  35. How would you read this measurement? This should be read as 105.00 grams (g.)

  36. The electronic/ digital balance: When using this balance, it is not necessary to estimate any places.

  37. 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 digit

  38. 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

  39. Known + Estimated Digits In 2.76 cm… • Known digits2and7are 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

  40. Learning Check . l8. . . . I . . . . I9. . . .I . . . . I10. . cm What is the length of the line? 1) 9.6 cm 2) 9.62 cm 3) 9.63 cm

  41. SIG FIGSAtlantic-Pacific • IF there is a Decimal Point Then anything to the right is significant • If a decimal Point is Absent, then moving the left the first number and everything after it are significant.

  42. How many Sig Figs Are there? • 0.43798 = • 150000= • 0.000015= • 1.00054= • 8675309= • 1500.00

  43. How many Sig Figs Are there? • 0.43798 = • 150000= • 0.000015= • 1.00054= • 8675309= • 1500.00

  44. Sig Fig Adding or Subtracting • Answers should have as many sig figs as the number with the least amount of Decimal Places that are in the problem. • Ex. • .67 g + 5.009 g= • 45.94 - 44.74 =

  45. Sig Figs Multiply and Divide • Look at the total number of sig figs in the problem.  • Report your answer to the smallest number of total sig figs. • Ex. • 8 x 4 = • 24.00 x 2.000 = • 12.00 x 3.000

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