# Dimensional Analysis/ Factor-label Method 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 2 1 1 = x 3 = 6 3 2 1 2 1 x = 2 3

3 2 x 15 = 3 2 15 x = 3 1 2 5 x = 10 1 1 Remember Algebra? ax 4z ax 4z x 4 4x x =

x = x = yz 3a yz 3a y 3 3y 2 METRIC PREFIXES LARGE MEGA (M) 1M KILO (K) = 1 X 106 1K = 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 NANO

1 = 1 X 109 n PICO 1 = 1 X 1012p 3 Examples of Equalities Conversion Factors 60 sec = 1 min 60 min = 1 hr 24 hr = 1 day 365 days = 1 yr 1 mile = 5,280 ft 1 ft = 12 in 1 in = 2.54 cm 1 gal = 3.785 L 1 gal = 4 qt

1 qt = 2 pint 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 4) DO THE MATH! 5 HOW MANY MINUTES ARE IN 4 HOURS? 60 MIN 4.0 HOURS X 1 HOUR =240 MIN

HOW MANY KILOGRAMS ARE IN 5 GRAMS? 1 Kg 5gX = 0.005 Kg 1000 g 6 CHANGE 286 cg TO Mg (BOTH UNITS HAVE PREFIXES SO MUST DO TWO CONVERSIONSONE TO BASE UNIT THEN TO OTHER PREFIX UNIT!) 286 cg X 1g 100 cg X 1 Mg = 0.00000286 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 = 2.54 cm 1 in 354.5 cmX 2.54 cm 139 in = 139.6 in 8