6th Grade Math Textbook, Fundamentals

 &KDSWHU

6-10

Dimensional Analysis

Objective To apply dimensional analysis • To use unit ratios to convert currency,

time, and Customary Units of length, capacity, and weight

Dan and Lin rode a high speed train that traveled at a rate
of 180 miles per hour (mi/h). What was the train’s speed in
feet per second (ft/s)?

To find the speed in feet per second, convert miles per hour
using dimensional analysis.

 is the conversion from one unit

system to another.

You are given the units for the rate of speed

as the ratio:.

In order to convert systems, you need to know:

• How many feet are in 1 mile?


• How many minutes are in 1 hour?


• How many seconds are in 1 minute?

Use these unit ratios: 1 mi : 5280 ft

1 h : 60 min

1 min : 60 s

These unit ratios are called , the

unit ratios needed to convert the given units.

Method 1 Convert by multiplying the given rate by

the conversion factors.

180 mi/h 



264 ft/s

Method 2 Convert using separate calculations.

• Convert miles to feet.
  If 1 mi 5280 ft, then 180 mi (180)(5280) ft.
  180 mi 950,400 ft


• Convert hours to seconds.
  If 1 h 60 min and 1 min 60 s, then 1 h (60)(60) s.
  1 h 3600 s

So .

The high speed train traveled at 264 feet per second.

conversion factors

Dimensional analysis

180

1

5280

1

11

388

11

mi

h

ft

mi

h

60 min

min

60 s

•••

180 mi

1 h

950,400 ft

3600 s

264 ft

1 s

264 ft

1 s

Cross off units that are the same in

the numerator and the denominator.

180 mi

1 h Customary Units of Length

1 foot (ft) 12 inches (in.)

1 yard (yd) 3 ft or 36 in.

1 mile (mi) 5280 ft or 1760 yd

Customary Units of Capacity

1 cup (c) 8 fluid ounces (fl oz)

1 pint (pt) 2 c

1 quart (qt) 2 pt

1 gallon (gal) 4 qt 128 fl oz

Customary Units of Weight

1 pound (lb) 16 ounces (oz)

1 ton (T) 2000 lb

Unit Conversions