Transcript Dimensional Analysis - Independent School District 196

Dimensional Analysis
The proper way to show the
conversion between 2 different units
of measurement
Dollars To Dimes
1 dollar = 10 dimes
5 dollars
10 dimes
1 dollar
50 dimes
How Many Bagels Are In 12 Dozen?
1 dozen = 12 units
12 dozen bagels
12 bagels
1 dozen bagels
144 bagels
Metric Conversions
1-Step
• If the base unit is found as the starting point
or ending point to a dimensional analysis
problem, it will be a 1-step problem
• Examples of base units include:
meters, seconds, liters, grams, bagels
m  cm
• How many centimeters are in 2.58 meters?
• 1-step problem because a base unit (m) is the
starting point
Remember…1 ALWAYS goes with the prefix!
1 cm = 10-2 m
2.58 m
1 cm
10-2 m
2.58 x 102 cm
dag  g
• How many grams are in 6.5 decagrams?
• 1-step problem because a base unit (g) is the
ending point
Remember…1 ALWAYS goes with the prefix! 1
dag = 101 g
6.5 dag
101 g
1 dag
6.5 x 101 g
s  ks
• How many kiloseconds are in 9.80 x 10-3
seconds?
• 1-step problem because a base unit (s) is the
starting point
Remember…1 ALWAYS goes with the prefix!
1 ks = 103 s
9.80 x 10-3 s
1 ks
103 s
9.80 x 10-6 ks
Practice 1-Step Metric Conversions
• 720 mg  g
• 4.58 x 105 μL  L
• 5.00 m  mm
Metric Conversions
2-Step
• If the base unit is not found as the starting
point or ending point to a dimensional
analysis problem, it will be a 2-step problem
• Always go the base unit as a first step
hm  dm
• How many decimeters are in 25.8 hectometers?
• 2-step problem because a base unit (m) is not the
starting point or ending point
• Go to the base unit (m) as a first step
Remember…1 ALWAYS goes with the prefix!
1 hm = 102 m
1 dm = 10-1 m
25.8 hm
102 m
1 dm
1 hm
10-1 m
2.58 x 104 dm
mL  ML
• How many megaliters are in 639 milliliters ?
• 2-step problem because a base unit (L) is not the
starting point or ending point
• Go to the base unit (L) as a first step
Remember…1 ALWAYS goes with the prefix!
1mL = 10-3 L
1 ML = 106 L
639 mL
10-3 L
1 mL
1 ML
106 L
6.39 x 10-7 ML
Practice 2-Step Metric Conversions
• 55 μs  Ms
• 6.55 x 10-4 km  mm
• 450 cg  hg
Sig Figs?
• The sig figs represented in the starting point
should be carried over to the ending point.
• Conversions are considered exact
measurements and should be used to
determine sig figs in the final answer.
Non-Metric Conversions
• A non-metric conversion will consist of 2
different base units.
How many inches are in a 92.5 centimeters?
1 inch = 2.54 cm
92.5 cm
1 in
2.54 cm
36.4 in
lbs  oz
• How many ounces are in 38.25 pounds
1 lb = 16 oz
38.25 lbs
16 oz
1 lb
612.0 oz
mm  yds
• 2090.0 mm  yds
1 mm = 10-3 m
2090.0 mm
10-3 m
1 mm
1 yd = .9144 m
1 yd
.9144 m
2.2857 yds
Mixed Practice
• 4.5 x 103 s  yrs
• 250 cal  J
• 6.72 mg  carats
km/s  mi/hr
3.8 km 1 mi
1s
60 s
1.609 km 1 min
60 min 8500 mi
1 hr
1 hr
Conversions & Calculation Practice
• 1.8 mm + 75 cm + .098 km = ______cm
• 10. cm3 + 50. mL + 35.8 L = _____mL