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### Dimensional Analysis

• In order to perform dimensional analysis, choose a conversion factor that causes the units you have to cancel and the units you want to remain.
• It is helpful to memorize these conversion factors.
•  Length 12 in = 1 ft 36 in = 1 yd 3 ft = 1 yd 5280 ft = 1 m Weight 16 oz = 1 lb 2000 lb = 1 t Capacity 8 fl oz = 1 cup 2 cups = 1 pt 4 cups = 1 qt 2 pt = 1 qt 4 qt = 1 gal

### Dimensional Analysis

Convert 2.4 miles into feet. Use the conversion factor [(5280 ft)/(1 mi)].
• 2.4 mi ×[(5280 ft)/(1 mi)] =
12,572 ft
Convert 2[3/4] pounds to ounces. Use the conversion factor [(16 oz)/(1 lb)].
• 2[3/4] lb ×[(16 oz)/(1 lb)] =
• [11/4] lb ×[(16 oz)/(1 lb)] =
• [11/1] lb ×[(4 oz)/(1 lb)] =
44 oz
Convert 7.2 cups to fl oz. Use the conversion factor [(8 fl oz)/(1 cup)].
• 7.2 cups ×[(8 fl oz)/(1 cup)] =
57.6 fl oz
Convert 13,400 lb to tons. Use the conversion factor [(2000 lb)/(1 t)].
• 13,400 lb ×[(1 t)/(2000 lb)] =
6.7 t
Find the unit rate for traveling 3,500 miles in 22.5 minutes.
• [(3,500 mi)/(22.5 min)] = [?/(1  min)]
• [(3,500 ÷22.5)/(22.5 ÷22.5)] = [?/1]
[(155.56 mi)/(1 min)]
A group project will require 30 hours of total work in order to be completed. If there are 5 people in the group working on the project at the same time, how long will the project take?
• [(30 hours)/(5 people)] =
6 hours
A scale needs 6 pounds on one side to balance out the other. How many 12-ounce weights will you need to balance the scale?
• 6 lb ×[(16 oz)/(1 lb)] = 96 oz
• 96 oz ÷ 12 oz =
8 weights
A quilt needs to be 6 feet long. How many 4-inch blocks of cloth will you need, length-wise, to make the quilt?
• 6 ft ×[(12 in)/(1 ft)] = 72 in
• 72 in ÷ 4 in =
18 blocks of cloth
[(15 gal)/(1 min)] = ?[pt/s]
• 2 pt = 1 qt
• 4 qt = 1 gal
• 1 min = 60 s
• [(15 gal)/(1 min)] ×[(4 qt)/(1 gal)] ×[(2 pt)/(1 qt)] ×[(1 min)/(60 s)] =
• [(120 pt)/(60 s)] =
[(2 pt)/s]
[(780 in)/(5 s)] = ?[m/days]
• 12 in = 1 ft
5280 ft = 1 m
60 s = 1 min
60 min = 1 hr
24 hr = 1 day
• [(780  in)/(5 s)] ×[(1 ft)/(12 in)] ×[(1 mi)/(5280 ft)] ×[(60 sec)/(1 min)] ×[(60 min)/(1 hr)] ×[(24 hr)/(1  day)] =
• [(67,392,000 m)/(316,800 days)] =
[(212.72 m)/day]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Dimensional Analysis

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What You'll Learn and Why 0:05
• Topics Overview
• Vocabulary 0:15
• Conversion Factor
• Dimensional Analysis
• Conversion Chart: Length 0:32
• Conversion Chart: in, ft, yd, and m
• Conversion Chart: Weight 0:49
• Conversion Chart: oz, lb, and t
• Conversion Chart: Capacity 0:59
• Conversion Chart: fl oz, cup, pt, qt, and gal
• Converting Units 1:17
• Example: Convert 1.3 Miles Into Feet
• Converting Units 3:14
• Example: Convert Pounds to Ounces
• Example: Convert Cups to Fluid Ounces
• Converting Units in a Rate 4:30
• Unit Rate: 2,200 m in 17.2 min
• Using Dimensional Analysis 8:06
• Example: Planning Project
• Extra Example 1: Converting Units 9:15
• Extra Example 2: Unit Rate 10:31
• Extra Example 3: Planning Project 12:15
• Extra Example 4: Converting Units 13:45