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Scientific Notation. Write 17,500 in scientific notation. 1.75 x 10 4 Write 0.0050 in scientific notation. 5.0 x 10 -3 (3.0 x 10 5 )(5.0 x 10 -2 )= (3.0 x 5.0) x 10 5+(-2). Metric (SI) Base Units. Length- meter Mass- kilogram Volume- liter (displacement)
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Scientific Notation Write 17,500 in scientific notation. 1.75 x 104 Write 0.0050 in scientific notation. 5.0 x 10-3 (3.0 x 105)(5.0 x 10-2)= (3.0 x 5.0) x 105+(-2)
Metric (SI) Base Units • Length- meter • Mass- kilogram • Volume- liter (displacement) - cm3 (L x W x H) • Temperature- Celsius C=5/9(F-32) F = 9/5C +32 - Kelvin 0◦C = 273 K
1 km = 1000m 1mm = 10-3 m 1pg =10-12 g • SI Prefixes mega 106 kilo 103 basic unit deci 10-1 centi 10-2 milli 10-3 micro 10-6 nano 10-9 pico 10-12
Significant Figures Indicate the uncertainty of a measurement
The significant figures in a measurement are all the digits that are known with certainty, plus the first digit that is uncertain.
Beginning zeros are not significant. • Ending zeros are only significant when there is a decimal.
Significant Figures • All nonzero digits are significant 43.5 • Zeros are significant when. . . • between two nonzero digits 120.01 • to the right of a decimal point and to the right of a nonzero digit. 30.00 • to the left of an expressed decimal point and to the right of a nonzero digit. 19,000. • Not significant when. . . • the zeros to the right of a decimal and to the left of a nonzero digit. 0.00056 • to the right of a nonzero digit but to the left of an understood decimal 109,000
Operations with significant figures • Multiplication and division The answer contains the same number of significant figures as the measurement with the least number of significant figures. • Addition and Subtraction The answer has the same number of decimal places as the measurement with the least number of decimal places.
xx x x x x Precision vs. Accuracy • Precision is the agreement between measurements. • Accuracy is the nearness of a measurement to its actual value. x x x xx x x x x Not precise, nor accurate Precise, not accurate Precise and accurate
37.53 5.8 These thermometers have different levels of precision. The increments on the left one are .2 but on the right one they are 1 . How should their temperatures be recorded?
Percent Error theoretical – experimentalx100% = theoretical Ex.: You analyze a sample of copper sulfate and find that it is 68% copper. The theoretical value is 80%. What is your percent error? 80-68 x 100% = 15% 80
Dimensional Analysis • Multiply your starting point by a conversion factor (equal to 1) • Units should cross out algebraically, leaving you with the unit desired. Ex.: Convert 2hr to min. Conversion factor is 1hr = 60min 2hr x 60min= 120 min 1 hr
mega(M) 106 kilo 103 basic unit deci 10-1 centi 10-2 milli(m) 10-3 micro(µ) 10-6 nano 10-9 pico 10-12 How many micrograms are in 18.4g? 18.4g x 1µg = 18.4x 106µg 10-6 g Notice: when the unit gets smaller (from g to µg), the number gets larger. Converting within the metric system
Practice problem How many seconds are in a day? Starting point: 1 day Conversion factors: 60 s = 1 min 60 min = 1hr 24 hr = 1 day 1 day x 24hr x 60 min x 60 s = 86,400s 1 day 1 hr 1 min
Rates • Convert 65mi/hr to km/s. 65mi x 1.61km x 1hr = .029 km/s hr 1mi 3600s
In Switzerland, gas prices are listed in Swiss Francs per liter. Convert the Swiss prices below to dollars per gallon.
Conversion factors needed: • Dollars to Francs: 1 SF = $.83 • Liters to gallons: 1 quart = 0.946 L 1 gallon = 4 quarts 1.71 SF x $.83 x .946L x 4 qt = $5.37 1 L 1 SF 1 qt 1 gal gal
Density Review If you knew the density and volume of a substance, could you figure out its mass?
If aluminum foil has a density of 2.70 g/cm3 and the mass of your sample is 1.65 g, what is the volume of your sample? • 1.65 g= .611 cm3 2.70 g/cm3
How could you then find the thickness of that foil? Volume = L x W x H In this case, the height is the thickness of the foil. Your measurements told you that the length was 15.30 cm and the width was 15.20 cm. So. . . V = L x W x H .611 cm3 = 15.30 cm x 15.20 cm x H .611 cm3= .0026268 cm 232.6 cm2 = .00263 cm
Thickness = .00263 cm An angstrom is 10-8 cm. How many angstroms would that be? .00263 cm x 1 angstrom= 2.63 x 105 Å 10-8 cm
Thickness Problem Steps • Find volume V = m/D • Find area a = L x W • Find thickness V/a