For more information, please see full course syllabus of Pre Algebra

Start learning today, and be successful in your academic & professional career. Start Today!

Loading video...

This is a quick preview of the lesson. For full access, please Log In or Sign up.

For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### 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.

Length12 in = 1 ft 36 in = 1 yd 3 ft = 1 yd 5280 ft = 1 m | Weight16 oz = 1 lb 2000 lb = 1 t | Capacity8 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.

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
- What You'll Learn and Why
- Vocabulary
- Conversion Chart: Length
- Conversion Chart: Weight
- Conversion Chart: Capacity
- Converting Units
- Converting Units
- Converting Units in a Rate
- Using Dimensional Analysis
- Extra Example 1: Converting Units
- Extra Example 2: Unit Rate
- Extra Example 3: Planning Project
- Extra Example 4: Converting Units

- 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

0 answers

Post by Daniel Wu on September 16, 2016

Pretty sure it's 5280 ft is one mile not one meter

0 answers

Post by Khanh Nguyen on February 16, 2014

In question 1 the answer is supposed to be 12672, not 12572

0 answers

Post by Madeline Johnson on November 29, 2012

Witch is the same as 3 3/4

0 answers

Post by Madeline Johnson on November 29, 2012

I did 7500 / 2000 and my answer is 3.75

1 answer

Last reply by: Professor Fung

Mon Sep 24, 2012 4:14 AM

Post by Michael Trow on September 24, 2012

5280 ft equals one meter? Maybe in US you don't use Meters I am 5f7 and half inches tall and I am 172 cm tall or 1.72 m tall your are about 1000 times off the real life measurement

2 answers

Last reply by: bo young lee

Tue Nov 27, 2012 9:03 PM

Post by aloosh aloosh on January 4, 2011

wrong answer again its 127.9

0 answers

Post by aloosh aloosh on January 4, 2011

5280ft =i MILE not meter