DIMENSIONAL ANALYSIS
DIMENSIONAL ANALYSIS

Is used to convert units of measurements.

Units for Mass
Weight-Pounds (lb)
 Weight-Ounces (oz)- 16 oz = 1 lb
 Grams (g)

Kilo (kg)- 1000
 Deci- 1/10
 Centi 1/100
 Milli- 1/1,000
 Micro- 1/100,000


Units for Volume





Gallons (gal)
Pints (pt)
Ounces (fl oz)
Liters (L) – kilo, deci, centi, milli…
Units for Length





Miles (mi)
Foot (ft)
Yard (yd) 1 yd = 3 ft
Inches (in) 1 in = 2.34 cm
Meters (m) – kilo, deci, centi, milli….
CONVERSION FACTORS

The guiding principle of dimensional analysis is
that you can multiply anything by “1” without
changing the meaning.

An equality set into a fraction formation = 1.



For example, if x = y, then x/y = 1 and y/x = 1.
Therefore, the equalities can be set into fractions and
multiplied to convert units.
These are called conversion factors

Ex: 1 in = 2.34 cm
1 𝑖𝑛
2.34 𝑐𝑚
=1
or
2.34 𝑐𝑚
1 𝑖𝑛
=1
CONVERTING

Ex: How many inches is 34.2 centimeters?
What do we know?
Known from question: 34.2 cm
Unknown from question: ? Inches
Conversion Factors: 1 inch = 2.34 cm so
34.2 cm
1 in
2.34 cm
1 𝑖𝑛
2.34 𝑐𝑚
= 14.6 in
or
2.34 𝑐𝑚
1 𝑖𝑛
CONVERTING

How many ounces are in 8.9 lbs?
What do we know?
Known from question: 8.9 lbs
Unknown from question: ? Ounces
Conversion factor: 1 lbs=16 oz
8.9 lbs
16 oz
1 lbs
1 𝑙𝑏𝑠
so 16 𝑜𝑧 or
16 𝑜𝑧
1 𝑙𝑏𝑠
= 142.4 oz
CONVERTING

How many meters is 84.1 yards. (1 m = 3.28 ft)
What do we know?
Known from question: 84.1 yards
Unknown from question: ? Meters
Conversion Factors:
1 m = 3.28 ft
3 ft = 1 yard
84.1 yd
3 ft
1m
1 yd
3.28 ft
= 76.9 m
CONVERTING

How many seconds are in 61 days?
What do we know?
Known from Questions: 61 days
Unknown from questions: ? Seconds
Conversion Factors:
1 day = 24 hours
61 days 24 hr
1 day
1 hour = 60 mins
60 mins
1 hr
60 secs
1 min
1 min= 60 seconds
= 5.27 x 106 secs
PRACTICE PROBLEMS

1. How many eggs are in 34 dozen?

2. How many feet are in 25 miles? (1 mile=1760 yd)

3. How many hours is 6235 seconds?

4. How many mL is 45 kL?

5. How many kg is 134 cg?

6. How many m are in 72 km?