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Measurement & Calculation

Measurement & Calculation. An Introduction. Scientific Inquiry: What it is & What it is not!. Scientific Notation. Scientific Notation- numbers are written in the form M x 10 n , where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number.

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Measurement & Calculation

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  1. Measurement & Calculation An Introduction Scientific Inquiry: What it is & What it is not!

  2. Scientific Notation • Scientific Notation- numbers are written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number. • 3,400 m = 3.4 x 103 m .0034 m = 3.4 x 10-3 m • In addition/subtraction, exponents (n) must be equivalent • In multiplication, exponents (n) are added. • In division, exponents (n) are subtracted.

  3. Guided Practice of Scientific Notation • Addition/Subtraction 5.2 x 106 L 9.3 x 10-4 J • + 3.1 x 106L - 7.1 x 10-4 J • 8.3 x 106 L 2.2 x 10-4 J Multiplication/Division (9.0 x 104 m)(6.0 x 102m) 54 x 106 m2 5.4 x 107m2 36 x 10-3 m /6.0 x 106 s 6 x 10-9 m/s

  4. Scientific Thinking Process ApplyingUsing knowledge to solve complex problems; inventing InferringPredicting patterns based on data formulating models; theorizing RelatingCause and effect relationships; space/time relationships; controlled experimentation OrganizingCategorizing, grouping, classifying Ordering: seriating and sequencing ComparingSensory comparisons, relative position comparisons; measurement (linear, volume, mass, quantity, temperature) CommunicatingSilent, oral, written, pictorial Observing Seeing, hearing, feeling, tasting, smelling

  5. Scientific Inquiry Earth is center of universe Claudis Ptolemy Sun is center of Universe Nicolas Copernicus A.D. 150 1543

  6. Measurement Mania! • Does size matter REALLY?!! What items require exact measurement to you? Quantity: Something that has magnitude, size, or amount

  7. Accuracy & Precision • Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. • Precision refers to the closeness of a set of measurements of the same quantity made in the same way.

  8. What was your error in your last prediction? Name some predictions- Percent error is calculated by subtracting the e xperimental value from the accepted value, dividing the difference by the accepted value, and then multiplying by 100. Percent Error = Valueaccepted – Valueexperimentalx 100 Valueaccepted

  9. Significant Figures • http://www.youtube.com/watch?v=9PeVHnjqbBc Significant Figures- numbers in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. Rules on Significant Figures- Non-zero numbers are significant (83.45) Captured zeros are significant. (bordered by nonzero numbers- like 703) Trailing zeros are significant IF there is a decimal (2.60; 400; 401.) Leading zeros are never significant (00.016)

  10. Identify the number of significant figures: 1) 3.0800 2) 0.00418 3) 7.09 x 10¯5 4) 91,600 5) 0.003005 6) 3.200 x 109 7) 250 8) 780,000,000 9) 0.0101 10) 0.00800 1)5 2)3 3)3 4)3 5)4 6)4 7)2 8)2 9)3 10)3 11) 13.01 + 10.1 = a. 23 b. 23.1 c. 23.11 12) 20.5 – 6.33 = a. 15 b. 14.2 c. 14.23 13) 22.1 + 14.2 = a. 30 b. 36 c. 36.3 14) 1.5 x 2 = a. 3 b. 3.0 c. 3.00 11) b. 12)b 13)c 14)a

  11. Sig Figs in action! Addition & Subtraction Multiplication & Division • When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. • Ex. 13.55 – 4.3 = 9.25 = 9.2 (round) • Whole numbers should be rounded so that the answer’s final digit should be rounded the same as that of the leftmost uncertain digit regardless of the number of places. • http://www.youtube.com/watch?v=5UjwJ9PIUvE&feature=related First determine the significant figures of the numbers of the problem. The least significant figure determines the number of significant figures in the product or quotient. Ex. 237/6 = 39.5 = 40

  12. Significant Figures Practice • Addition/subtraction- when adding or subtracting decimals, the answer must have the same places as the least significant figure. You cannot produce a more accurate number than you started! Ex. 6.32 g 8.0 g + 1.2 g - 7.2 g • Multiplication/division • The answer can have no more significant figures than are in the measurement with the fewest number of significant figures. • Ex. 1.10 mm x 6.0 mm = 6.6 mm2 because 6.60 mm2 is more precise than our measurements indicate. 7.5 g 0.8 g

  13. SI Measurement:Le Systeme International d’Unites • Base Units • Length- m meter m • Mass kg kilogram kg • Time t second s • Temperature T Kelvin K • Amount of substance n mole mol • Electric current l ampere A • Luminous intensity Iv candela cd

  14. SI Prefixes

  15. Can you see estimate these sizes? How many meters tall is Sherron Collins? How many centimeters tall is Collins? Can you convert between units? He is 5’11” tall. There are 39” in a meter. There are 12” in a foot. The answer: He is 71” tall which is 1.32 m . How many cm?

  16. Weight vs. Mass • What the difference between weight & mass? Picture of Earth & Moon as seen from Mars! Weight- measure of the gravitational pull on matter Mass- measure of the quantity of matter in a substance

  17. Derived SI Units • Derived units are combinations of the SI base quantities. • Volume is the amount of space occupied by a substance. • Some combination units have their own name: • Heat measurement: • Joule= force x length newton * m • Pressure measurement: • Pascal=Pa= force/area • newton/m2 = kg/m * s2

  18. Derived units- great for applications! Quantity Symbol Unit Derivation Area A m2 length x width Volume V m3 length x width x height Density D kg/m3 mass/volume Molar mass M kg/mol mass/amt of sub. Concentration c mol/L amt of sub./volume Molar volume V m3/mol volume/amt of sub. Energy E Joule force x length Note: mol = mole

  19. Breakdown of derived units Area= length x width 2 cm x 8 cm = 16 cm 2 2 cm 8 cm 6 m 2 m Volume = length x width x height 4m x 2m x 6m= 48 m3 4 m 6 m 2 m 4 m 24 kg = 0.5 kg/m3 4m x 2m x 6m Density = mass/volume 24 kg

  20. Molar mass = mass amt. of sub. 8 kg = 2 kg 4 mol mol 8 kg 4 moles of NaCl Concentration= Amt. of sub volume 3 mol = 3 mol 1 L L 3 moles Co 1000 ml 0.4 moles caffeine Molar Volume= volume amt of substance 0.4 L = 1 L 0.4 mol mol 0.4 L

  21. Density= Mass Volume http://www.youtube.com/watch?v=fqLCwuKMBMA

  22. What are things you convert daily?

  23. Conversion Units 1 dozen donuts = 12 donuts If I had 3 dozen donuts, how many donuts do I have? 3 dozen| 12 donuts = 36 donuts 1 dozen If I had 48 donuts, how many dozen donuts do I have? 48 donuts|1 dozen=4 dozen donuts 12 donuts

  24. Conversion Factors • A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other. • Always go back to the units you know well • Use LOGIC! 1 m = 100 cm = 0.001 km How many km is it to KU if you are 7800 m away? 1 L = 1000 ml = 100 cl How many ml are in 6.2 L of Mt. Dew? 1 kg = 1000 g = 1,000,000 mg How many g are in 500,000 mg? 7.8km 6200 ml 500 g

  25. Proportionality • Direct Proportional- 2 quantities are directly proportional to each other if dividing one by the other gives a constant value • y = k • X • Inverse Proportionality- • 2 quantities if their product is constant • Example: xy = k

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