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Scientific Notation

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

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  1. 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)

  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

  3. 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

  4. Significant Figures Indicate the uncertainty of a measurement

  5. The significant figures in a measurement are all the digits that are known with certainty, plus the first digit that is uncertain.

  6. Beginning zeros are not significant. • Ending zeros are only significant when there is a decimal.

  7. 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

  8. 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.

  9. 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

  10. 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?

  11. 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

  12. 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

  13. 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

  14. 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

  15. Rates • Convert 65mi/hr to km/s. 65mi x 1.61km x 1hr = .029 km/s hr 1mi 3600s

  16. In Switzerland, gas prices are listed in Swiss Francs per liter. Convert the Swiss prices below to dollars per gallon.

  17. 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

  18. Density Review If you knew the density and volume of a substance, could you figure out its mass?

  19. 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

  20. 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

  21. 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

  22. Thickness Problem Steps • Find volume V = m/D • Find area a = L x W • Find thickness V/a

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