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Measurements

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Measurements: Definitions Measurement: –comparison between measured quantity and accepted, defined standards (SI) Quantity: –property that can be measured and described by a pure number and a unit that names the standard

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Measurement Types: –Qualitative: describe a substance without using numbers (measurements). –Quantitative: require measurement to be made and have to be described by a QUANTITY (number and unit)

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Measurement Requirements Know what to measure Have a definite agreed upon standard Know how to compare the standard to the measured quantity (tool)

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Types of measurement Quantitative- –use numbers + units to describe the measured quantity. Examples: the density of iron is 7.8 g/cm 3. Qualitative- –use description (language) without numbers to describe the measurement Quantitative or qualitative? –4 feet _____________________ –extra large _____________________ –Hot _____________________ –100ºF _____________________

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Measuring Numbers without units are meaningless. The measuring instrument limits how good the measurement is

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Scientific Notations A shortcut method for writing very large and very small numbers using powers of ten 602,000,000,000,000,000,000,000,000 The number is written as M x 10 n –n is + number = large numbers (>0) –n is - number = small numbers (<0)

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Accuracy, Precision, and Certainty: How good are the measurements? Accuracy how close the measurement is to the actual value Precision how well can the measurement be repeated. (How well do the measurements agree with each other?)

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Let’s use a golf anaolgy

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Accurate?No Precise?Yes

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Accurate?Yes Precise?Yes

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Precise?No Accurate?Maybe?

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Accurate?Yes Precise?We cant say!

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In terms of measurement Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. Were they precise? Were they accurate?

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Assessing Uncertainty The person doing the measuring should asses the limits of the possible error in measurement

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Significant figures (sig figs) How many numbers mean anything When we measure something, we can (and do) always estimate between the smallest marks. 21345

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Significant figures (sig figs) The better marks the better we can estimate. Scientist always understand that the last number measured is actually an estimate 21345

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Significant Digits and Measurement Measurement –Done with tools –The value depends on the smallest subdivision on the measuring tool Significant Digits (Figures): –consist of all the definitely known digits plus one final digit that is estimated in between the divisions.

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Sig Figs Only measurements have sig figs. Counted numbers are exact A dozen is exactly 12 A piece of paper is measured 11 inches tall. Being able to locate, and count significant figures is an important skill.

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Measured Value Uncer- tainty Ruler Division Known digits Estimated digit 1.07 cm+/-0.01 cm0.1 cm1, 07 3.576 cm+/-0.001 cm0.01 cm3,5,76 22.7 cm+/- 0.1 cm1 cm2, 27 Significant Figures: Examples

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Significant Rules examples What is the smallest mark on the ruler that measures 142.15 cm? –____________________ 142 cm? –____________________ 140 cm? –____________________ Does the zero count? We need rules!!!

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Rules of Significant Figures Pacific: If there is a decimal point present start counting from the left to right until encountering the first nonzero digit. All digits thereafter are significant. Atlantic: If the decimal point is absent start counting from the right to left until encountering the first nonzero digit. All digits are significant.

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Sig figs. How many SF in the following measurements? 1.458 g 2.4085 g 3.4850 g 4.0.0485 g 5.0.004085 g 6.40.004085 g

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Sig Figs. 7.405.0 g 8.4050 g 9.0.450 g 10.4050.05 g 11.0.0500060 g

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Rounding rules Look at the number next to the one you’re rounding. 0 - 4 : leave it 5 - 9 : round up Round 45.462 to: a) four sig figs b) three sig figs c) two sig figs d) one sig fig

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Calculations with Significant Figures

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Multiplication and Division Same number of sig figs in the answer as the least in the question 1) 3.6 x 653 = 2350.8 3.6 has 2 SF 653 has 3 SF answer can only have 2 SF Answer: 2400

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Multiplication and Division Same rules for division practice 4.5 / 6.245 4.5 x 6.245 9.8764 x.043 3.876 / 1983 16547 / 714

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Practice 4.8 + 6.8765 520 + 94.98 0.0045 + 2.113 6.0 x 10 2 - 3.8 x 10 3 5.4 - 3.28 6.7 -.542 500 -126 6.0 x 10 -2 - 3.8 x 10 -3

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The Metric System: SI System An easy way to measure

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The Metric System Easier to use because it is a decimal system Every conversion is by some power of 10. A metric unit has two parts –A prefix and a base unit. prefix tells you how many times to divide or multiply by 10.

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SI Prefixes Exapetatera Gigamegakilo HectadecaUnit Centimillimicro Nanopicofemto Atto Check blackboard for details

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Fundamental Units SI UnitNameAbbreviation LengthMeterM MassKilogramKg TimeSeconds Temperature KelvinK Electric current AmpereA Quantity of matter MoleMol luminosityCandelaCd

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Mass Quantity of matter The same in the entire universe Based on Pt/Ir alloy standard 1gram is defined as the mass of 1 cm 3 of water at 4 ºC. 1000 g = 1000 cm 3 of water at 4 ºC 1 kg = 1 L of water 4 ºC

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Measuring Temperature Celsius scale. water freezes at 0ºC water boils at 100ºC body temperature 37ºC room temperature 20 - 25ºC 0ºC

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Measuring Temperature Kelvin starts at absolute zero (-273 º C) degrees are the same size C = K -273 K = C + 273 Kelvin is always bigger. Kelvin can never be negative. Absolute zero: temp. at which a system cannot be farther cooled.

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