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Measurements in Experiments 1.2 pp 10-19 Mr. Richter Agenda Turn in Posters Warm-Up Discuss Energy Paragraphs Finish Yesterday’s Notes Questions about the Quiz? Introduction to the Metric System Notes (Day 1): Measurement The Metric System (SI) Metric Prefixes and Scientific Notation Day 2: Accuracy Precision Significant Figures Objectives: We Will Be Able To… List basic SI units and the quantities they describe. Convert measurements into scientific notation. Distinguish between accuracy and precision. Use significant figures in measurements and calculations. Warm-Up: There are 5280 feet in a mile. There are 1000 meters in a kilometer. How many feet are in 4 miles? How many meters are in 4 kilometers? For Tomorrow’s Quiz You Should: Review your notes Review the slides online Pay special attention to things I have repeated (Like vocab, objectives, homework problems…) Bring a sharpened pencil and be ready to go at the bell tomorrow Measurement What are Measurements? Measurements tell us how much of what kind of stuff we have. Measurements require two things: A quantity – how much A dimension (units) – what kind UNITS MATTER! My amount of wealth differs greatly if I have 30 million dollars or 30 million yen I can’t say “I live four away from here.” It only makes sense if I say “four miles” or “four kilometers”. Système Internationale (SI) aka The Metric System All scientists and most countries use the SI or metric system. Why? Because it is easy to convert between large and small units. And to use scientific notation. The SI system has three base units (p. 11): Meter – length Kilogram – mass Second – time All other units are combinations or derivations of these three. Metric Prefixes The SI uses metric prefixes and scientific notation to accommodate extreme values of the base units. You will be required to memorize: nano micro milli centi kilo- mega- Homework for Tonight p14 #1-5 Warm-Up Work by yourself in your notes to answer each question. How many meters is: 1. 42 kilometers 2. 4.2 kilometers Remember to think in terms of being realistic: are meters larger or smaller than the original unit? 3. 0.42 kilometers If you can, try to do this from memory; without the prefix charts. 7. 4.2 centimeters 4. 4200 centimeters 5. 420 centimeters 6. 42 centimeters Agenda Warm-Up Accuracy and Precision Review Quiz Significant Figures Set Up Portfolios Review Homework More On Metric Conversions Scientific Notation Objectives: We Will Be Able To… List basic SI units and the quantities they describe. Convert measurements into scientific notation. Distinguish between accuracy and precision. Use significant figures in measurements and calculations. Converting with Metric Prefixes (Another Method) 1 mm = 10-3 m, therefore: Make sure units cancel out. Bad: To convert between units, Good: multiply by the conversion factor. Using Units Units must agree. A fancy way of saying that the units used to express a measurement must match. For example: Don’t use kilograms to measure length. Duh. Sometimes people will use different units of distance to measure the same thing, like area. Avoid and convert: feet-meters centimeter-meters Scientific Notation Review Scientific Notation Used in conjunction with metric prefixes to indicate the size of a measurement. To convert to scientific notation: slide decimal point to the right of the first non-zero value 0.000345 3.45 267000 2.67000 then multiply by a power of 10 to compensate for the shifted decimal point 0.000345 3.45 x 10-4 267000 2.67000 x 105 Your Turn Convert the following values into scientific notation: How did you do? 1. 4.2 x 103 1. 4200 2. 3.406 x 102 2. 340.6 3. 2 x 10-2 3. 0.02 4. 6.50 x 10-3 4. 0.00650 Warm-Up Express the following How did you do? measurements in scientific 3.46 x 102 m notation: 2.4 (or 2.40 or 2.400) x 103 g 346 meters 1.8 x 10-3 m/s 2400 grams 0.0018 meters/second Scientific Notation The real reason for scientific notation: not just because we’re sick of writing zeros. Scientific notation allows us to compare the sizes of numbers almost instantaneously. Which number is bigger? 23000000000000000 or 170000000000000000 How much easier is it in scientific notation? 2.3 x 1016 or 1.7 x 1017 Accuracy and Precision Accuracy Describes how close a measured value is to the true value of the quantity measured. Errors in accuracy come from: human error – incorrect use of instrument or science using a tape measure incorrectly reading a thermometer at the wrong level instrument error – the device used to take a measurement doesn’t work the tape measure or thermometer is broken Precision Refers to the degree of exactness with which a measurement is made and stated. Errors in precision come from the limitations of an instrument, not human error or calibration. For example: if the scale at the doctor’s office measures only to the nearest kilogram, then the doctor cannot be expected to state your mass to the nearest tenth of a kilogram. Accuracy vs. Precision: Length The length of a 18-cm pencil is measured three times with a ruler by three different people: The length is measured to be about 18 cm each time: accurate but not precise. The length is measured to be 16.92 cm, 20.31 cm, and 17.75 cm respectively: precise but not accurate. The length is measured to be 17. 98 cm, 18.03 cm, and 17.96 cm: both accurate and precise. Significant Figures What numbers matter? (Summary of rules pp. 17-19) Significant Figures (SigFigs) Significant figures indicate the degree of precision with which a measurement was taken. For example: 23 meters vs. 23.0 meters. What’s the difference? The same number mathematically, but the latter is more precise. The measurement was taken with a more precise instrument. Significant Figures comes down to: Which zeros don’t matter? Any in front of non-zero digits: 0.0008 Any at the end of a number but to the left of the decimal: 2000 Significant Figures and Scientific Notation Scientific notation tells the difference between significant and insignificant figures. For example: 200 could have 1 significant figure or 3. In scientific notation: 200 = 2 x 102, or 200 = 2.00 x 102 It is easy to see which measurement is more precise written in scientific notation. Calculations with Significant Figures Adding: the sum should have the same number of digits to the right of the decimal as the least precise measurement. 250.4 + 112 ≠ 362.4 (indicates too much precision) 250.4 + 112 = 362 Multiplying: the product should have the same number of significant figures as the least precise measurement. 4.6 x 6.7 ≠ 30.82 (indicates too much precision) 4.6 x 6.7 = 31 Note: Your calculator doesn’t get sig figs. Your Turn Try p. 28 #20, a-d Wrap-Up: Did we meet our objectives? List basic SI units and the quantities they describe. Convert measurements into scientific notation. Distinguish between accuracy and precision. Use significant figures in measurements and calculations. Homework Due Wed: p19 #1-4