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The 7 base units from which all other units are derived:

Lecture 2 Fall 2007. Units of measurement. Sections 1.4 through 1.6. 1.4. Units of Measurement. Must have units – SI units are the Systeme International . This has 7 base units from which all other units are derived:. The 7 base units from which all other units are derived:.

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The 7 base units from which all other units are derived:

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  1. Lecture 2 Fall 2007. Units of measurement. Sections 1.4 through 1.6.1.4. Units of Measurement.Must have units – SI units are the Systeme International. This has 7 base units from which all other units are derived:

  2. The 7 base units from which all other units are derived: • Physical Unit abbreviation • Quantity_______________________ • Mass kilogram kg • Length Meter m • Time second s or sec • Temperature Kelvin K • Amount of • Substance Mole mol

  3. Prefixes are used to indicate decimal fractions or multiples of the above units: • Prefix Abbr. meaning example • Giga G 109 gigameter • Mega M 106 megameter • Kilo k 103 1 kilometer • Deci d 10-1 1 deciliter • Centi c 10-2 1 centiliter • Milli m 10-3 1 milligram • Micro μ 10-6 1 microgram • Nano n 10-9 1 nanometer • Pico p 10-12 1 picogram • Femto f 10-15 1 femtosecond

  4. Derived SI units: • Volume: The volume of a cube is given by the lengths of its sides multiplied together. Thus, the volume of anything has the units m3, or cm3. The most commonly used unit of volume in chemistry is the liter, which is a dm3. 1 mL = 1 cm3 is interchangeable. a Volume = a x b x c Units = meters x meters x meters = m3 or = cm x cm x cm = cm3 or ml or cc c b

  5. Density: • Density is mass/volume. Commonly expressed as gm/ml or gm/cc. • Densities of some common substances: • __________________________________ • Air 0.0001 g/cc Ethanol: 0.79 • Water: 1.00 Table salt: 2.16 • Iron: 7.9 Gold: 19.32

  6. 1.5. Uncertainty in Measurement: • Exact numbers: e.g. number of inches in a foot, number of people in the lecture theater. Are usually defined numbers. • Inexact Numbers: These are measured numbers, which always have a degree of uncertainty. Suppose ten students measure the mass of the same dime on ten different balances. They will all get slightly different values. (=2.2811 g. a quarter weighs 5.57 g))

  7. Precision and accuracy: Precision is how closely a set of measurements agree with each other. Accuracy is how closely the set of measurements agree with the correct or true value. good accuracy good precision

  8. Significant Figures: Suppose you measure the weight of a dime on a balance stated to be accurate to 0.0001 g. You could report the weight as 2.2405 ± 0.0001 g. Measured quantities are reported in such a way that only the last digit is uncertain. All digits of a measured quantity are called significant figures.

  9. To determine the number of significant figures in a number start counting digits from the left to the right. Note:Zeroes at the end or in the middle of a number are significant, those at the beginning are not. 0.000103 three significant figures 1.030 four “ “ 1.0300 x 105 five “ “

  10. Significant Figures in Calculations: For multiplication and division:The result contains the same number of significant figures as the measurement with the fewest significant figures: e.g. area = 6.221cm x 5.2 cm = 32.3492 = 32 cm2. Only two significant figures

  11. Addition and Subtraction. For addition and subtraction:The result contains the same number of decimal places as the result with the fewest decimal places. e.g. 20.42 + 1.322 + 83.1 = 104.842 = 104.8

  12. Dimensional Analysis Converting inches into cm: Conversion factor: same quantity but in different units the units to be eliminated go on opposite sides of the fraction

  13. Dimensional Analysis Converting m/min into m/s: Conversion factor the units to be eliminated go on opposite sides of the fraction

  14. Dimensional Analysis More than one conversion: A car travels 12 km per liter of gasoline. How many many miles per gallon will it go? => Convert 12 km/L into mi/gallon => first, convert length units: km into mi, second, convert volume units: L into gallons

  15. Dimensional Analysis ? or ?

  16. Dimensional Analysis Place conversion factor so units to be removed will cancel

  17. Dimensional Analysis Note: 12 kilometers has only two significant figures, so answer must have only two significant figures

  18. Conversions involving squared and cubic units: The volume of a container is 5.3 m3. What is the volume in cm3? • Convert m3 into cm3 • Conversion factor = 100 cm or 100 cm 1 meter 1 m Vol in cm3 = 5.7 meter3 x 100 cm x 100 cm x 100 cm 1 meter 1 meter 1 meter = 5,700,000 cm3 (note: 1 m3 = 1 m x 1 m x 1 m)

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