### Dimensional analysis

```DIMENSIONAL
ANALYSIS
WARM-UP
Four more than three times a number is one less than
four times the number. What is the number?
4  3n  4n  1
3n  4n  1  4
 n  5
n5
Dimensional Analysis
• Dimensional Analysis is a procedure used to convert from
one unit of measurement to a different unit of
measurement.
• To do dimensional analysis, you must understand what is
meant by a unit fraction.
Unit Fraction
• A unit fraction is any fraction in which the numerator and
denominator contain different units and the value of the
fraction is 1.
• The table on the next slide shows many unit fractions
involving U.S. customary units.
Examples of Unit Fractions
Example: How many inches are in 5
feet?
12in.
5 ft x
 60in.
1 ft.
8 oz is how many pounds? (Hint: 1
pound = 16 oz)
1 pound 8 1
8 oz x
  pounds
16oz
16 2
15 yards to feet
3 feet
15 yardsx
 (15x3) ft  45 ft
1 yard
4 feet to inches
12in
4 ft x
 48in
1 ft
6 pints to cups (Hint: 1 pint = 2 cups)
2 cups
6 pts x
12cups
1 pt
42 inches to feet
1 ft
42
42in x

 3.5 ft
12in 12
John drives on the interstate 60 miles per hour.
How many feet per second is he traveling?
mi 5280 ft
1hr
1 min 316800 ft
60
x
x
x

 88 ft
sec
hr
1mi
60 min 60 sec
3600 sec
Kim can scan 20 items per minute. How
many can she scan in 15 seconds?
• Find how many she
can scan per second:
20
items 1Minute 20 1 items
x


sec
Minute 60 sec
60 3
• Multiply by 15
seconds.
1
x15  5 items
3
Jared can work 54 math problems in 1 hour. How
many problems can he work in 10 minutes?
• Figure the amount per
minute first:
problem s 1hr
54
54
x

hr
60Min 60
9 problem s
Re ducesto
Min
10
• Now multiply that
amount by 10 minutes.
9 problems
x10 Min  9 problems
Min
10
A machine makes 360 gadgets every 24 hours. How many
gadgets does it make every 20 minutes.
• Find the # of gadgets
per minute first:
x
 .315
24hours 60 Min
Min
• Next, multiply by 20
minutes to get the # of
.315
x 20 Min  6.3 gadgets
Min
Perry’s car can travel an average of 22 miles on 1 gallon of
gas. How many miles can his car travel on 1 quart of gas?
(Hint: 1 gallon = 4 quarts)
22m iles 1 gallon 22
x
 m iles/ quart
gallon 4 quarts 4
or
5.5 m iles
quart
```