Mastering Dimensional Analysis for Unit Conversion
"Learn how to master dimensional analysis and the factor-label method for unit conversion with the help of fractions, algebra, metric prefixes, examples of equalities, and step-by-step instructions. Explore practical conversions like time, weight, length, and more."
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Presentation Transcript
DIMENSIONAL ANALYSIS/ FACTOR-LABEL METHOD TREAT UNITS AS FACTORS, WHICH CAN BE CANCELLED MUST KNOW YOUR EQUALITIES OR CONVERSION FACTORS CHOOSE THE EQUALITY THAT CANCELS OUT THE ORIGINAL UNIT 1
Remember Fractions? 2 3 2 3 2 6 =1 1 2 1 2 x = 3 =1 x 3 2 3 2 3 15 1 2 1 5 1 x 15 = x = x = 10 Remember Algebra? 4z 3a yz 3a ax yz ax 4z x y 4 3 4x 3y x = x = x = 2
METRIC PREFIXES LARGE MEGA (M) KILO (K) = 1 X 106 1 M = 1 X 103 1 K SMALL DECI CENTI MILLI MICRO NANO PICO = 1 X 101 d 1 = 1 X 102 c 1 = 1 X 103 m = 1 X 106 1 1 = 1 X 109 n 1 = 1 X 1012p 1 3
Examples of Equalities Conversion Factors 60 sec = 1 min 60 min = 1 hr 24 hr = 1 day 365 days = 1 yr 1 gal = 3.785 L 1 gal = 4 qt 1 qt = 2 pint 1 mile = 5,280 ft 1 lb = 454 g 1 lb = 16 oz 1 oz = 28.35 g 1 ft = 12 in 1 in = 2.54 cm 4
STEPS: 1) BEGIN WITH KNOWN 2) DECIDE ON AN EQUALITY 3) ARRANGE UNITS TO CANCEL OUT ORIGINAL UNITS 4) DO THE MATH! 5
HOW MANY MINUTES ARE IN 4 HOURS? 60 MIN X = 1 HOUR 4.0 HOURS 240 MIN HOW MANY KILOGRAMS ARE IN 5 GRAMS? 1 Kg 1000 g 5 g X = 0.005 Kg 6
CHANGE 286 cg TO Mg (BOTH UNITS HAVE PREFIXES SO MUST DO TWO CONVERSIONS ONE TO BASE UNIT THEN TO OTHER PREFIX UNIT!) 1 g X X = 100 cg 1 Mg 0.00000286 286 cg Mg 1 x 106 g or 2.86 x 10-6 Mg 7
CHANGING UNITS TO CHANGE FROM ENGLISH TO METRIC UNITS, USE CHART ON PG 38. HOW MANY INCHES ARE IN 354 cm? 1 in 354 cm X = 139 in 2.54 cm 1 in 354.5 cm 139.6 in X = 2.54 cm 8
