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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).

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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. Addition and subtraction: all numbers must be changed to the same exponent. Then add or subtract the numbers, attaching the common exponent. ex.: 8.3 x 102 + 5.7 x 103 0.83 x 103 +5.7 x 103 6.53 x 103 6.5 x 103

  3. 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

  4. SI Prefixes Giga 109 Mega 106 kilo 103 basic unit deci 10-1 centi 10-2 milli 10-3 micro 10-6 nano 10-9 pico 10-12

  5. From DOE

  6. Significant Figures Indicate the uncertainty of a measurement

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

  8. 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

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

  10. 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.

  11. Operations with significant figures • Multiplication and division Sample 1: 24 cm x 31.8 cm = 763.2 cm2 answer: 760 cm2 Sample 2: 8.40 g ÷ 4.2 ml = 2 g/ml answer: 2.0 g/ml

  12. Addition and Subtraction Sample 1: 49.1 g + 8.001 g = 57.101 g answer: 57.1 g Sample 2: 81.350 m – 7.35 m = 74 m answer: 74.00 m

  13. 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

  14. 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?

  15. 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

  16. Derived Units • Measurements derived from basic units. • Area= L x W (m2) • Volume = L x W x H (cm3) • Density = m/V (g/cm3)

  17. Calculations 1. What is the density of a substance whose mass is 3.0 grams and its volume is 15cm3? 3.0 grams = .20 g/cm3 15 cm3 2. Cobalt has a density of 8.90 g/cm3. What volume would 17.8 g of cobalt have? D=m/V so V=m/D V = 17.8 g = 2.00 cm3 8.90 g/cm3

  18. 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

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

  20. 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

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