GUESS AND
CHECK
I. GUESS
  Mr. Rea does not actually promote
“guessing” as it is generally a terrible
strategy.
  GUESS is an acronym that you will use to
help you get started when solving tough
dimensional analysis problems.
  Let’s start with a relatively easy problem:
What is the density of a rock with a mass of
4 grams and a volume of 3 milliliters?
I. GUESS
  1) G = given
  Identify the given value(s).
 
m = 4 g and v = 3 mL
I. GUESS
  2) U = unknown
  What is the quantity we want?
density
 g/mL
 
I. GUESS
  3) E = equation
  Sometimes formula, sometimes dimensional
analysis
  D = m/v
I. GUESS
  4) S = substitution/set up
  If necessary, substitute variables for the
given values. Otherwise, cancel units.
  D = 4 g / 3 mL
I. GUESS
  5) S = solution
  It’s only complete with a value and units.
 
D = 1.3 g/mL
II. Check
 Check means making sure your answer
makes sense.
 Question: What is the density of a
metal with a mass of 86.531 g and a
volume of 40.785 mL?
 a) 0.3 g/mL
 b) 2.1 g/mL
 c) 1000 g/mL
II. Check
 How many micrometers are in 0.45
meters?
 
 a) 4.5 × 105 µm
 b) 4.5 × 10–7 µm
III. Problem Types
  1) One-step: How many meters are 5.7 × 105
mm?
  1) 570 (5.7 × 102)
III. Problem Types
 2) Multi-step: How many cg in 35 kg?
 2) 3,500,000 (3.5 × 106)
III. Problem Types
 3) Double Unit: If the density of a piece
of wood is 0.622 g/mL, what is the
density in kg/cL?
 3) 0.00622 (6.22 × 10–3)
III. Problem Types
 4) Squared/Cubed Units: How many
nm2 are in 42.7 mm2?
 4) 4.27 × 1013 nm2