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# Metrics and Measurement

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Presented by Sharon Williams in the ACT2 strand at CAST 2010. Houston, Texas.

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### Metrics and Measurement

1. 1. Scientific Measurement
2. 2. Scientific Measurement Distinguish between quantitative and qualitative measurements. List SI units of measurement and common SI prefixes. Distinguish between the mass and weight of an object. Convert measurement to scientific notation. Distinguish among the accuracy, precision, and error of measurement. Identify the number of significant figures in a measurement and in the result of calculation. Identify and calculate derived units. Calculate the density of an object from experiment data. TEKS: 2A, 2B, 2C, 2D, 2E, 3C, 3D, 3E, 4B, 4C
3. 3. Quantitative vs. Qualitative Observations Qualitative – observations made with adjectives “The water is clear and cool.” Quantitative – observations that include a measurement or other numeric data “There are 40mL of water.”
4. 4. Two parts of measurements 1. Quantity – indicates size or magnitude (how much?)2. Unit – tells us what is to be measured and compares it to a previously defined size (of what?) Measurements must have both a quantity and a unit to be valid.
5. 5. International System of Units  Length – meter  Mass – kilogram  Temperature – Kelvin  Energy – joule  Amount of a substance – mole  Electric current - ampere  Volume – m3  Density – g/cm3  Weight - Newton
6. 6. Commonly Used Prefixes in the Metric SystemPrefix Meaning Exponentmega (M) 1 000 000 106kilo (k) 1000 103hecto (h) 100 102deka (da) 10 101deci (d) 1/10 10-1centi (c) 1/100 10-2milli (m) 1/1000 10-3micro (µ) 1/1 000 000 10-6nano (n) 1/1 000 000 000 10-9pico (p) 1/1 000 000 000 000 10-12
7. 7. Conversion Factors Conversion factors are equalities written in ratio form: 1 km = 1000m 1km = 1000 m 1000 m 1 km Choose the format that allows you to cancel the original units and leave the new units. Ex. 2.5 km = ________ m You would choose 1000 m km
8. 8. Conversion Factors Make sure that you have a valid equality before writing your conversion factor. Which of these equalities are correct? 1 m = 1 x 10-6 µm 1 m = 1 x 106 µm 1 x 10-6 m = 1µm
9. 9. 1 dm Important Equalities 10 cm 1 dm 1 dm3 = 1000cm3 10 cm 1mL = 1cm3 = 1cc 1dm3 = 1000 mL = 1L100 dm3 = ‗‗‗‗nm3
10. 10. Conversion Practice Problem List in order – largest to smallest a. 1 dm3 b. 1 µL c. 1 mL d. 1 L e. 1 cL f. 1 dL
11. 11. Derived Units Derived units are formed from a combination of other units. Examples include: m/s & km/hr (speed), cm3 & dm3(volume), J/g· C (specific heat), g/mol (molar mass), g/cm3 & kg/m3 (density)
12. 12. Density Density is the ratio between the mass and volume of an object. Density = Mass or D=m Volume V Density is an intensive physical property.
13. 13. Density ProblemsA student finds a shiny piece of metal that shethinks is aluminum. She determined that themetal has a volume of 245 cm3 and a mass of612 g. Calculate the density. Is the metalaluminum?The density of silver at 20ºC is 10.5 g/cm3.What is the volume of a 68 g bar of silver?
14. 14. Density Problems Continued A weather balloon is inflated to a volume of 2.2 x 103 L with 37.4 g of helium. What is the density of helium, in grams per liter. A plastic ball with a volume of 19.7 cm3 has a mass of 15.8 g. What is its density? Would the ball sink or float in a container of water?
15. 15. Specific GravitySpecific Gravity = Density substance (g/cm3) Density water (g/cm3)
16. 16. Making Measurements
17. 17. Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. (how close) Precision refers to the degree of agreement among several elements of the same quantity. (how repeatable)
18. 18.  Target (a) shows neither accuracy or precision. Target (b) shows precision, but not accuracy. Target (c) shows both accuracy and precision.
19. 19. Uncertainty in Measurement A digit that must be estimated is called uncertain. The last digit in a measurement always shows uncertainty.
20. 20. Significant Digits Significant Digits show the degree of certainty in a measurement. Not all digits in a number show certainty, therefore, all digits are not significant.
21. 21. Counting Significant DigitsRule 1: Nonzero integers always count as significant digits.  3456 has 4 “sig digs”
22. 22. Counting Significant DigitsRule 2: Leading zeros do not count as significant figures.  0.0486 has 3 “sig figs”
23. 23. Counting Significant DigitsRule 3: Captive zeros always count as significant figures.  16.07 has 4 “sig digs”
24. 24. Counting Significant DigitsRule 4: Trailing zeros are significant only if the number contains a decimal point.  9.300 has 4 “sig figs”
25. 25. Counting Significant Digits Exact numbers have an infinite number of significant figures. Exact numbers include counting numbers and conversion factors. Examples:  12 students  1m = 100 cm
26. 26. Practice Problems Determine the number of significant figures. a. 12 kilometers b. 0.010 m2 c. 507 thumbtacks d. 0.070020 m e. 10800 m f. 5.00 m3. g. 2.340 x 103 cm h. 6.02 x 1023 atoms
27. 27. Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation.  6.38 cm 2.0 cm = 12.76 cm2  13 (2 sig figs)
28. 28. Multiplication and Division Your answer can only have the least number of significant figures in your data.a. 2.0 mL x 3.00 mLb. 8432 m = 12.5 m
29. 29. Rules for Significant Figures in Mathematical Operations Addition and Subtraction: # sig figs in the result equals the number of decimal places in the least precise measurement. 6.8 cm + 11.934 cm + 3.7556 cm = 22.4896 cm  22.5 cm (1 digit after decimal - 3 sig figs)
30. 30. Addition and Subtraction Count the decimal places. You can only have in your answer the least number of decimal places that is seen in your data. 1.0 1 7.00 1 1.00 + 2.00 - 1.001 + 0.5+ 1.000
31. 31. Rounding RulesIf the digit following Then the last digit Example (rounded to 3the last digit to be should: sig dig’s)retained is:greater than 5 be increased by 1 38.68 g to 38.7 gless than 5 stay the same 12.51 m to 12.5 m5, followed by nonzero be increased by 1 4.8851 cm to 4.89 cmdigit(s)5, not followed by be increased by 1 2.975 kg to 2.98 kgnonzero digit(s), and (because 7 is odd)preceded by an odd digit5, not followed by Stay the same 2.985 kg to 2.98 kgnonzero digit(s), and the (because 8 is even)preceding significantdigit is even
32. 32. Measurement Tips
33. 33. Measurement Tools•Distance = Meter Sticks & Metric Tapes•Volume = Graduated Cylinder•Time = Stopwatch•Mass = Balance•Weight = Spring Scale
34. 34. Mass vs. Weight Mass is the amount of matter in an object; weight is the effect of gravity on a mass. Mass is measured on a balance; weight is measured with a scale. Mass remains constant at all locations; weight varies with change in gravitational pull.
35. 35. Volume 1. Never measure in a beaker. They are for estimation only!2. Place the graduated cylinder on a level surface and read the bottom of the meniscus. 3. Check the scale of the graduated cylinder. Different scales for different sizes! 4. Use displacement to find the volume of irregular solids.
36. 36. Mass 1. Make sure the balance is on a level surface. 2. Use the same balance in the same place for all parts of a procedure.3. DO NOT MOVE A BALANCE ONCE IT IS ZEROED!
37. 37. Length Rulers & meter sticks wear on the ends – start at a point other than zero. Choose the unit most reasonable for the item you are measuring – make sure you convert your number accordingly.