Transcript dimensional analysis

Problem-Solving Strategy for Unit Conversions
DIMENSIONAL ANALYSIS
DIMENSIONAL ANALYSIS
Problem-solving strategy to convert measurements
in one unit to an equivalent quantity in another unit
How many kilograms are in 150 lbs?
How many calories are in 42 joules?
How many inches are in 127 miles?
How many seconds are in 22 days?
CONVERSION FACTORS
Identify the relationship between two values
with different units that express the same
quantity
 Provide the step-by-step directions to go from
the starting point to the ending point

1
min = 60 s
 1 hr = 60 min
 12 in = 1 ft
1
cal = 4.184 J
 1 kg = 2.2 lbs
 1 g = 1000 mg
CONVERSION FACTORS
Such factors are ratios and can be expressed
as fractions
 The fractions may be written in two ways and
always equal a value of 1
 If you have one dozen eggs, how many eggs do
you have? 12 eggs
 Therefore, 1 dozen eggs = 12 eggs

1 dz eggs
=1
12 eggs
12 eggs
=1
1 dz eggs
DIMENSIONAL ANALYSIS

KNOW WHERE YOU ARE GOING


KNOW WHERE YOU START


Identify (circle) the given in the problem statement.
DRAW THE BRIDGE


Identify (underline) the unknown in the problem
statement.
Outlines the path to be taken from start to finish
STEP-BY-STEP DIRECTIONS

Determined by the applicable conversion factors.
It’s all in the units!
DIMENSIONAL ANALYSIS
How many kilograms are in 150 lbs?
What conversion factor applies to this problem?
1 kg = 2.2 lbs
 Expressed as fractions:

1 kg
2.2 lbs

2.2 lbs
1 kg
Write the UNKNOWN, start with the GIVEN, and
then draw the BRIDGE to connect the two
quantities
BRIDGES

Bridges provide the structure for the problemsolving strategy of dimensional analysis
STEP-BY-STEP DIRECTIONS
DRAW THE BRIDGE
UNKNOWN =
KNOW WHERE YOU ARE GOING
GIVEN
CONVERSION
FACTOR
KNOW WHERE YOU START
FROM LBS TO KG
How many kilograms are in 150 lbs?
STEP-BY-STEP
DIRECTIONS
1 kg = 2.2
lbs
DRAW THE BRIDGE
UNKNOWN
kilograms =
KNOW WHERE YOU ARE GOING
GIVEN
150
lbs
CONVERSION
1 kg
FACTOR
2.2 lbs
KNOW WHERE YOU START
FROM LBS TO KG
How many kilograms are in 150 lbs?
When the only unit left standing
matches the unknown,
the bridge is complete.
kilograms =
150 lbs
1 kg
2.2 lbs
Now, it’s time for the math.
FROM LBS TO KG
kilograms =
150 lbs
1 kg
2.2 lbs
MULTIPLY all numbers on the top of the bridge
150 x 1 = 150
DIVIDE by each number on the bottom
150 / 2.2 = 68.18181818
The unit left standing is the unit of the answer: kg
CHECK number of significant figures in GIVENs
and express answers to same number of SF
ROUND to 2 SF  68 kg
DIMENSIONAL ANALYSIS
How many calories are in 42 joules?
• 1 calorie = 4.184 joules
How many inches are in 127 miles?
• 12 inches = 1 foot
• 5,280 feet = 1 mile
How many seconds are in 22 days?
• 60 seconds = 1 minute
• 60 minutes = 1 hour
• 24 hours = 1 day