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Meaningful digits in a MEASUREMENT Exact numbers are counted, have unlimited significant figures If it is measured or estimated, it has sig figs. If not it is exact. All numbers except zero are significant. Some zeros are, some aren’t
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In between other sig figs does Before the first number doesn’t After the last number counts if ◦ it is after the decimal point ◦ the decimal point is written in 3200 2 sig figs 3200. 4 sig figs
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Multiplication and division, same number of sig figs in answer as the least in the problem Addition and subtraction, same number of decimal places in answer as least in problem.
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Scientific Method Metric System Uncertainty
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A way of solving problems Observation- what is seen or measured Hypothesis- educated guess of why things behave the way they do. (possible explanation) Experiment- designed to test hypothesis leads to new observations, and the cycle goes on
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After many cycles, a broad, generalizable explanation is developed for why things behave the way they do Theory ◦ Also regular patterns of how things behave the same in different systems emerges Law ◦ Laws are summaries of observations
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Theories have predictive value. The true test of a theory is if it can predict new behaviors. If the prediction is wrong, the theory must be changed. Theory- why Law - how
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Observations Hypothesis Experiment Law Theory (Model) Prediction Experiment Modify
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Every measurement has two parts ◦ Number ◦ Scale (unit) SI system (le Systeme International) based on the metric system Prefix + base unit Prefix tells you the power of 10 to multiply by - decimal system -easy conversions
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Base Units Mass - kilogram (kg) Length- meter (m) Time - second (s) Temperature- Kelvin (K) Electric current- ampere (amp, A) Amount of substance- mole (mol)
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giga- G 1,000,000,00010 9 mega - M 1,000,00010 6 kilo - k 1,00010 3 deci-d0.1 10 -1 centi-c0.01 10 -2 milli-m0.001 10 -3 micro-m0.000001 10 -6 nano-n0.000000001 10 -9
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Mass is measure of resistance to change in motion Weight is force of gravity. Sometimes used interchangeably Mass can’t change, weight can
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Basis for significant figures All measurements are uncertain to some degree Precision- how repeatable Accuracy- how correct - closeness to true value. Random error - equal chance of being high or low- addressed by averaging measurements - expected
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Systematic error- same direction each time ◦ Want to avoid this ◦ Better precision implies better accuracy ◦ you can have precision without accuracy ◦ You can’t have accuracy without precision
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Using the units to solve problems
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Use conversion factors to change the units ◦ Conversion factors = 1 ◦ 1 foot = 12 inches (equivalence statement) ◦ 12 in = 1 = 1 ft. 1 ft. 12 in ◦ 2 conversion factors multiply by the one that will give you the correct units in your answer.
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11 yards = 2 rod 40 rods = 1 furlong 8 furlongs = 1 mile The Kentucky Derby race is 1.25 miles. How long is the race in rods, furlongs, meters, and kilometers? A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?
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Science fiction often uses nautical analogies to describe space travel. If the starship U.S.S. Enterprise is traveling at warp factor 1.71, what is its speed in knots? ◦ Warp 1.71 = 5.00 times the speed of light ◦ speed of light = 3.00 x 10 8 m/s ◦ 1 knot = 2000 yd/h exactly
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Apothecaries (druggists) use the following set of measures in the English system: ◦ 20 grains ap = 1 scruple (exact) ◦ 3 scruples = 1 dram ap (exact) ◦ 8 dram ap = 1 oz. ap (exact) ◦ 1 dram ap = 3.888 g ◦ 1 oz. ap = ? oz. troy What is the mass of 1 scruple in grams?
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The speed of light is 3.00 x 10 8 m/s. How far will a beam of light travel in 1.00 ns?
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A measure of the average kinetic energy Different temperature scales, all are talking about the same height of mercury. Derive a equation for converting ºF toºC
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0ºC 32ºF 0ºC = 32ºF
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100ºC212ºF 100ºC = 212ºF 0ºC 32ºF 0ºC = 32ºF
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100ºC212ºF 0ºC 32ºF 100ºC = 212ºF 0ºC = 32ºF 100ºC = 180ºF
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100ºC212ºF 0ºC 32ºF 100ºC = 212ºF 0ºC = 32ºF 100ºC = 180ºF 1ºC = (180/100)ºF 1ºC = 9/5ºF
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ºC ºF
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ºC ºF (0,32)= (C 1,F 1 )
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ºC ºF (0,32) = (C 1,F 1 ) (120,212) = (C 2,F 2 )
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Ratio of mass to volume D = m/V Useful for identifying a compound Useful for predicting weight An intrinsic property- does not depend on what the material is
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An empty container weighs 121.3 g. Filled with carbon tetrachloride (density 1.53 g/cm 3 ) the container weighs 283.2 g. What is the volume of the container?
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AA 55.0 gal drum weighs 75.0 lbs. when empty. What will the total mass be when filled with ethanol? density 0.789 g/cm 3 1 gal = 3.78 L 1 lb = 454 g
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