DIMENSIONAL ANALYSIS FACTORLABEL METHOD TREAT UNITS AS FACTORS

DIMENSIONAL ANALYSIS/ FACTORLABEL 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 2 1 1 = x = 3 6 3 2 1 x = 2 3 3 2 x 15 = 3 2 15 x = 3 1 2 5 x = 10 1 1 Remember Algebra? ax 4 z x 4 4 x x = x = yz 3 a y 3 3 y 2

METRIC PREFIXES • LARGE • MEGA (M) 1 M • KILO (K) = 1 X 106 1 K = 1 X 103 • SMALL • DECI 1 = 1 X 101 d • CENTI 1 = 1 X 102 c • MILLI 1 = 1 X 103 m • MICRO 1 = 1 X 106 μ • NANO 1 = 1 X 109 n • PICO 1 = 1 X 1012 p 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 ft = 12 in 1 in = 2. 54 cm 1 lb = 454 g 1 lb = 16 oz 1 oz = 28. 35 g 4

STEPS: 1) BEGIN WITH KNOWN 2) DECIDE ON AN EQUALITY 3) ARRANGE UNITS TO CANCEL OUT ORIGINAL UNITS 5

HOW MANY MINUTES ARE IN 4 HOURS? 60 MIN 4. 0 X 1 = 240 MIN HOURS HOUR HOW MANY KILOGRAMS ARE IN 5 GRAMS? 1 Kg 5 g X = 0. 005 Kg 1000 g 6

CHANGE 286 cg TO Mg (BOTH UNITS HAVE PREFIXES SO MUST DO TWO CONVERSIONS…ONE TO BASE UNIT THEN 1 g TO OTHER 1 Mg PREFIX 286 cg X X = 0. 00000286 Mg UNIT!) 100 cg 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 = 139 in 354 cm X 2. 54 cm 1 in 354. 5 cm. X = 2. 54 cm 139. 6 in 8