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Unformatted text preview: Chapter 3: Fundamental Measurements Measurement Components of Measurement Numerical quantity Unit Name of substance For example, 325.0 mL water Numerical quantity unit Name of substance Metric System Also called the International or SI system. Based on Units of 10 SI base Units Other units derived from base units Prefixes indicating power of ten SI Units Quantity Name Symbol Length meter m Mass kilogram kg Temperature Kelvin K Time second s Amount mole mol Common Metric Prefixes Prefix Symbol Decimal Exponential Mega M 1,000,000 10 6 Kilo k 1000 10 3 Centi c 0.01 102 Milli m 0.001 103 Micro 0.000001 106 Metric Units of Length Base Unit is the meter (m), a little longer than a yard. Other common Units: Centimeter, cm; 1 cm = 0.01m, ~ 0.4 inch Kilometer, km; 1 km = 1000 m, ~5/8 mile Millimeter, mm; 1 mm = 0.001 m, thickness of a dime. Insert Fig. 3.4 Units of Length Dimensional Analysis (Also called the factorlabel method) To convert a measurement from one unit to another, multiply the known quantity and unit(s) by a conversion factor to equal the desired quantity and unit(s): Known quantity and unit(s) X Conversion Factor(s) = Quantity with desired unit(s) Converting Units Using Conversion Factors Equivalencies yield two conversion factors: For example : 1 ft = 12 in 1ft/12 in = 1 or 12 in/1 ft = 1 How many inches in 5 ft? Number of inches = 5ft x = 12 in 1 ft 60 in. Considerations in Choosing Conversion Factors: The chosen conversion factor cancels all units except those required for the answer. Set up the calculation so that the unit you are converting from (beginning unit) is on the opposite part of the conversion factor (numerator or denominator) from the unit you are converting to (final unit) . Formulas beginning unit x final unit beginning unit = final unit Mi x ft mi = ft Choosing the correct conversion factor Choose the conversion factor which will yield the correct units in the denominator and numerator after the units are cancelled. Problem: How many cm are in 50 m? 1. Unit equivalency: 1 cm = 0.01 m 2. Conversion factors: 1cm/0.01m or 0.01m/1cm 3. In the answer, you want cm in the numerator so choose 1 cm/0.01m. Finish the Problem 4. Multiply given by chosen conversion factor: Answer = Given x Conversion factor Cm = 50 m x 0.01 m 1 cm = 5000 cm 5. Cancel units to get correct answer Conversion Factors May Be Multiplied Together in Series Example: Convert 179,800 s to days. Solution: Plan: s min hours days Conversion equivalents: 1 min = 60 s, l hr = 60 min, 1 day = 24 hr Conversion factors: 1 min/60 s, 1 hr/60min , 1 day/ 24 hr 179800 s x 1min/60s x 1hr/60 min x 1 day/24hr = 2.08 days Ratios with New Final Unit in Denominator: Final unit 1 Beginning unit X Beginning unit Final unit 2 = Final unit 1 Final unit 2 mi x h min = mi min h Problem Which Has New Final Unit in Denominator...
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 Spring '08
 Butler

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