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Measurements and Calculations Chapter 2

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Units of Measurement Measurements involve NUMBER and UNIT Represent a quantity: has magnitude, size, or amount Gram = unit of measurement Mass = quantity

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Units of Measurement Scientists around the world agree on one system… –International System of Units (le Systeme International d’Unites) –SI units –Built from seven base units

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SI Base Units

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Units of Measurement

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Metric Prefixes – make units easier to use Make the unit smaller or larger Unit = prefix + base unit Table pg. 35

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Mass Measures quantity of matter SI unit: kilogram, kg ______ kg = _____ g gram used for smaller masses Weight: measure of gravitational pull

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Length SI unit: meter, m Longer distances: kilometer, km _______ km = _______ m Shorter distances: centimeter, cm _______ m = ________ cm

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Volume SI unit: m 3 A derived unit: combination of base units by multiplying or dividing SI unit for Area: l x w = m x m = m 2 Volume: l x w x h = m x m x m = m 3 Also: liters (L), mL, dm 3 and cm 3 1 L = 1 dm 3 = 1000mL = 1000 cm 3

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Derived Units

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Scientific Notation Put the numbers in the form a x 10 n a has one # to left of decimal If # is bigger than 1 + exponent If # is less than 1 - exponent

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Scientific Notation Review: Write in scientific notation 32,700 0.0003412 3.901 x 10 -6 4.755 x 10 8

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

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Significant figures (sig figs) Better marks better estimate. Last number measured actually an estimate 21345

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Sig Figs What is the smallest mark on the ruler that measures 142.15 cm? 142 cm? 140 cm? Does the zero mean anything? (Is it significant?) They needed a set of rules to decide which zeroes count.

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Sig Figs. 405.0 g 4050 g 0.450 g 4050.05 g 0.0500060 g

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Sig Figs Only measurements have sig figs. Counted numbers are exact – infinite sig figs A dozen is exactly 12 Conversion factors: 100 cm = 1 m

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Problems 50 has only 1 significant figure if it really has two, how can I write it? Scientific notation 5.0 x 10 1 2 sig figs Scientific Notation shows ALL sig figs

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Rounding rules Round 454.62 to four sig figs –to three sig figs –to two sig figs –to one sig fig

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Calculations 1.165.86 g + 4.091g - 140 g + 27.32 g 2.(35.6 L + 2.4 L) / 4.083 = 3.2.524 x (16.408 m – 3.88 m) = Answers: 57g9.31 L31.62 m

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Sig figs. How many sig figs in the following measurements? 458 g 4085 g 4850 g 0.0485 g 0.004085 g 40.004085 g

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Density Density = massD = m volume V Units: g/cm 3 or g/mL but SI unit is kg/m 3 derived unit Used to identify substances Varies with temperature As temp. increases density…

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Density

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Density Examples If a metal block has a mass of 65.0 grams and a volume of 22 cubic centimeters, what is the density of the block? D = m V D = 65.0 g = 3.0 g/cm 3 22 cm 3

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Density Examples Aluminum has a density of 2.7 g/cm 3. What volume of aluminum has a mass of 60 grams? D = M V 20 cm 3

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Density Examples Gold has a density of 19.3 g/cm 3. A block of metal has a mass of 80 g and a volume of 12 cm 3. Could this block be a piece of gold? No, because this block has a density of 7 g/cm 3s

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Unit Conversions

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Given information in one unit need to find the equivalent in another unit 1.Identify what’s given 2.Organize plan of attack 3.Carry out plan WITH UNITS!!

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Conversion factors “A ratio of equivalent measurements.” Start with two things that are the same. 1 m = 100 cm Can divide by each side to come up with two ways of writing the number 1.

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Conversion factors 100 cm1 m= 100 cm

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Conversion factors 1 1 m= 100 cm

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Conversion factors 1 1 m= 100 cm =1 m

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Conversion factors 1 1 m= 100 cm = 1 m 1

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Conversion Factors Unique way of writing the number 1. Does NOT change the VALUE, it changes the UNITS.

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Write the conversion factors for the following kilograms to grams feet to inches 1 L = 1 dm 3 = 1000mL = 1000 cm 3

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Let’s See How They Work We can multiply by a conversion factor creatively to change the units. 13 inches is how many yards?

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Let’s Try Some! 323 mm = _____ nm 3.2 miles = _____ in 250 gallons = _____ mL 15 days = _______ min

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More Unit Conversions More Involved

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Derived Unit Conversions 54.3 cm 3 = ______ m 3 7.54 ft 2 = _______ in 2

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Derived Unit Conversions 125.3 m/s = ______ mi/hr 625 g/mL = ______ kg/m 3 100 km/hr = ______ mi/hr

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Where do these measurements come from? Recording Measurements

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Making Good Measurements We can do 2 things: 1.Repeat measurement many times - reliable measurements get the same number over and over - this is PRECISE

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Making Good Measurements 2. Test our measurement against a “standard”, or accepted value - measurement close to accepted value is ACCURATE Video - 46

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Measurements are Uncertain 1.Measuring instruments are never perfect 2.Skill of measurer 3.Measuring conditions 4.Measuring always involves estimation –Flickering # on balance –Between marks on instrument

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Estimating Measurements

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Error Probably not EXACTLY 6.35 cm Within.01 cm of actual value. 6.35 cm ±.01 cm 6.34 cm to 6.36 cm

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Calculating Percent Error Compares your measurement to accepted value Negative if measurement is small Positive if measurement is big

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Calculating Percent Error What is the % error for a mass measurement of 17.7g, given that the correct value is 21.2g?

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Direct Proportions Two quantities are directly proportional if dividing one by the other gives a constant y x “y is proportional to x” Gen. Eqn: y = k x Ex: mass and volume… constant is…

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Direct Proportions Solve for y: y = k x Look familiar? Eqn for a straight line: y = mx + b Slope is the constant

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Direct Proportion

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Inverse Proportions Two quantities are inversely proportional if their product is a constant “y is proportional to 1 divided by x” Gen eqn: xy = k Ex: speed and travel time

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Inverse Proportion Graph is called “hyperbola”

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Calculations Convert 3.23 x 10 4 kg to g. Give answer with correct sig. figs. How many miles are in 450,000 in?

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Calculations What is the mass of an object with a density of 25.98 g/mL and a volume of 4.2 mL? What is the density of a 430 g object that takes up 25.5 cm 3 ?

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