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## Measurements and Calculations

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**Measurements and Calculations**Chapter 2**Units of Measurement**• Measurements involve NUMBER and UNIT • Represent a quantity: has magnitude, size, or amount • Gram = unit of measurement • Mass = quantity**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**Units of Measurement**• Metric Prefixes – make units easier to use • Make the unit smaller or larger • Unit = prefix + base unit • Table pg. 35**Mass**• Measures quantity of matter • SI unit: kilogram, kg • ______ kg = _____ g • gram used for smaller masses • Weight: measure of gravitational pull**Length**• SI unit: meter, m • Longer distances: kilometer, km • _______ km = _______ m • Shorter distances: centimeter, cm • _______ m = ________ cm**Volume**• SI unit: m3 • A derived unit: combination of base units by multiplying or dividing • SI unit for Area: l x w = m x m = m2 • Volume: l x w x h = m x m x m = m3 • Also: liters (L), mL, dm3 and cm3 • 1 L = 1 dm3 = 1000mL = 1000 cm3**Scientific Notation**• Put the numbers in the form a x 10n • a has one # to left of decimal • If # is bigger than 1 + exponent • If # is less than 1 - exponent**Scientific Notation**• Review: Write in scientific notation 32,700 0.0003412 3.901 x 10-6 4.755 x 108**1**2 3 4 5 Significant Figures (sig figs) • How many numbers mean anything? • When we measure, we can (and do) always estimate between the smallest marks.**Significant figures (sig figs)**• Better marks better estimate. • Last number measured actually an estimate 1 2 3 4 5**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.**Sig Figs.**• 405.0 g • 4050 g • 0.450 g • 4050.05 g • 0.0500060 g**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**Problems**• 50 has only 1 significant figure • if it really has two, how can I write it? • Scientific notation • 5.0 x 101 2 sig figs • Scientific Notation shows ALL sig figs**Rounding rules**• Round 454.62 to four sig figs • to three sig figs • to two sig figs • to one sig fig**Calculations**• 165.86 g + 4.091g - 140 g + 27.32 g • (35.6 L + 2.4 L) / 4.083 = • 2.524 x (16.408 m – 3.88 m) = Answers: 57g 9.31 L 31.62 m**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**Density**• Density = mass D = m volume V • Units: g/cm3 or g/mL but SI unit is kg/m3 • derived unit • Used to identify substances • Varies with temperature • As temp. increases density…**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/cm3 22 cm3**Density Examples**• Aluminum has a density of 2.7 g/cm3. What volume of aluminum has a mass of 60 grams? • D = M V 20 cm3**Density Examples**• Gold has a density of 19.3 g/cm3. A block of metal has a mass of 80 g and a volume of 12 cm3. Could this block be a piece of gold? • No, because this block has a density of 7 g/cm3s**Unit Conversions**• Given information in one unit need to find the equivalent in another unit • Identify what’s given • Organize plan of attack • Carry out plan WITH UNITS!!**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.**1 m**100 cm 100 cm 100 cm Conversion factors =**Conversion factors**1 m = 1 100 cm**1 m**= 100 cm 1 m 1 m Conversion factors 1 m = 1 100 cm**Conversion factors**1 m = 1 100 cm = 100 cm 1 1 m**Conversion Factors**• Unique way of writing the number 1. • Does NOT change the VALUE, it changes the UNITS.**Write the conversion factors for the following**• kilograms to grams • feet to inches • 1 L = 1 dm3 = 1000mL = 1000 cm3**Let’s See How They Work**• We can multiply by a conversion factor creatively to change the units . • 13 inches is how many yards?**Let’s Try Some!**• 323 mm = _____ nm • 3.2 miles = _____ in • 250 gallons = _____ mL • 15 days = _______ min**More Unit Conversions**More Involved**Derived Unit Conversions**• 54.3 cm3 = ______ m3 • 7.54 ft2 = _______ in2**Derived Unit Conversions**• 125.3 m/s = ______ mi/hr • 625 g/mL = ______ kg/m3 • 100 km/hr = ______ mi/hr**Where do these measurements come from?**Recording Measurements**Making Good Measurements**• We can do 2 things: • Repeat measurement many times - reliable measurements get the same number over and over - this is PRECISE**Making Good Measurements**2. Test our measurement against a “standard”, or accepted value - measurement close to accepted value is ACCURATE Video - 46**Measurements are Uncertain**• Measuring instruments are never perfect • Skill of measurer • Measuring conditions • Measuring always involves estimation • Flickering # on balance • Between marks on instrument**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**Calculating Percent Error**• Compares your measurement to accepted value • Negative if measurement is small • Positive if measurement is big**Calculating Percent Error**• What is the % error for a mass measurement of 17.7g, given that the correct value is 21.2g?**Direct Proportions**• Two quantities are directly proportional if dividing one by the other gives a constant • yx “y is proportional to x” • Gen. Eqn: y = k x • Ex: mass and volume… constant is…**Direct Proportions**• Solve for y: y = k x • Look familiar? • Eqn for a straight line: y = mx + b • Slope is the constant