1.05 Dimensional Analysis or Unit Factor Method

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1.05 Dimensional Analysis or

Unit Factor Method

Dr. Fred Garces

Chemistry 100

Miramar College

12in = 1 ft

1 in = 2.54 cm

1 dime= 10 pennies

100 yd = 300 ft

*If you plan to be in the nursing field please go to the following url-

http://www.alysion.org/dimensional/analysis.htm

Read the context in this website to appreciate the importance in dimensional analysis in all type of calculation applications.

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Dimensional Analysis

Unit Conversion-Factor

Factor Label method

Ratios which are equivalent to the number 1 such as 12in/1ft

or 60 min/1 hr or 5280 ft/1 mi. are called unit factors, or

conversion factors. They are the key to most of the

calculations in this course. What you need to remember is

that the numerator and denominator of conversion factors

must always represent equivalent quantities.

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Communicating in a foreign land

Guadeloupe 0.05%, China 0.83% and Italy 29% speak English

Consider traveling abroad

Travel to Italy; How do you communicate?

Cab fare is 17.25 €!to the hotel, how much is it in $ ?

Suppose you are abroad and you want to communicate to the locals but you do not speak their language. How can you make your intentions known? One way is to use a translator. Another type of translator is the currency exchange.

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Basic Idea

The Basic idea of conversion factors is to change the

units that are given in a problem to units that is

being sought.

Given

Unit

Desired Goal

Unit

Speak English Accomplished goal

Translator

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Liras to dollars

How much is

€

17.25 in dollars?

Need to know currency exchange:

€

_{0.69 = $ 1.00 (Translator)}

Given

information

Translator

Goal

€

17.25 *

$ 1 . 00

€

0.69 = $

Currency Exchange rate

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Misc Conversion factors.

Banker has $100 to purchase a wedding cake but the baker doesn’t want his money instead, the baker needs 1 day tutoring for his son to pass the SAT. In this town the banker found the following tradesman, how can the banker secure a wedding cake?

Occupation Skill Need .

1. Baker 1 wedding cake 1 day tutoring

2. Plumber 1 hr labor 25lb stag

3. Carpenter Roofing labor 3 hr computer help 4. Farmer1 50 bushel corn $100

5. Farmer2 1 25 lb hog 50lb fish

6. Brew master 2 kegs beer Fix car radiator 7. Jewel smith Labor to craft necklace 4 hr house keeping 8. Auto mechanic car repair 1 25lb hog

9. Teacher 1 day tutoring fix broken necklace 10. Computer tech 3 hr computer setup 50 bushels corn 11. Fisherman 50lb fish Fix roof

12. Hunter 25lb stag 2 keg beer 13. Housekeeper 4 hrs house keeping 1 hr plumber

14. Banker $100 wedding cake

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Misc Conversion factors.

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Misc Conversion factors.

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Misc Conversion factors.

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Misc Conversion factors.

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The Basis of Conversion Factor

€

1 ∗ Anything = Anything

1

1 ∗ Anything = Anything

1 doz = 12 thus 12

1 doz

=

1 doz

12 = 1

Therefore

1 doz

12 ∗ Anything = Anything

!

Likewise

€

0.69 =

$1.00

€

0.69 12in = 1 ft

1 in = 2.54 cm

1 dime= 10 pennies

100 yd = 300 ft

$1.00

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Example: Distance to closes star.

How many miles is the closest star, Proxima Centauri, 4.2 Light Years (LY) ?

4.2 Light year∗ 365.25 day

1yr

∗

24hr

1day

∗

60min

1hr

∗

60sec

1min

∗

186,282 mi

1sec

= 2.5e13mi

Work it out

Conversion factors:

3.0 •10

10

_{cm / s or 186, 282 mi / hr}

365 days = 1 year

24 hr = 1 day

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Other Conversion factors.

Length

1 cm = 0.394 in 1 m = 39.4 in = 3.24 ft = 1.08 yd 1 in = 2.54 cm = 0.0833 ft 1 ft = 30.5 cm = 0.305m = 12 in 1 yd = 91.44 cm = 0.9144m = 3 ft =36 in

Volume

1 cm3_{= 1cc = 1 ml} 1 L = 1000ml = 1000 cm3_{= 1.057 qt} 1 qt = 0.946 L 1gal = 4 qt = 3.78 L

Mass

1 g = 0.0353 oz = 0.00220 lb. 1 Kg = 1000 g = 2.20 lb. 1 mt = 1000 Kg = 2200 lb. = 1.10 ton 1 lb = 454 g = 0.454 Kg 1 ton = 2000lb = 908 Kg = 0.908 mt

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Exercise on Dimensional Analysis

Suppose the exchange rate for the yen is 77 Yen / $1.00. If gold at the

Tokyo exchange is 140K Yen an ounce, how much will 50.0 gram cost in

euro. (453.9 gram = 1.00 lb., 16 oz. = 1.0 lb..)

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• • Number of Tallies, i.e., 5 fingers, 176 students.

• **• *Definition of numbers**

-– 

i.e., Exactly 1 m = 100 cm, or 1 in = 2.54 cm

• • Power of 10 in exponential notation

– 

i.e., 10

6

but practical to express numbers as 10

6.4 (exponential calc)

– 

*Define conversion versus measured conversion.

II Accuracy, Precision & Significant Figures

These type of numbers contain unlimited significant figures

(do not influence the number of significant figures in the final answer).

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18 1.05 Dimensional Analysis and Calculations

January 10

• 

One last important note

:

• 

-Conversion factor comes in two forms, the first are conversion factors from

definitions. Examples are, 60 min = 1 hr, 100cm = 1m, 5280 ft = 1 mile, 1 gal =

3.785 L, 100 pennies = $1.00.

-Other conversion factors are based on measured values. 65.0 mph

(65.0 mi = 1 hr) , $10/hr (10 $ = 1 hr), 0.76Euro/$ (0.76 euro = 1.00$)

• 

-Measured conversion factors

do have

defined significant figures

unlike

defined conversion factors that have infinite number of significant figures.

• Thus in the problem; If a runner for 139.9 minutes at 11 mph, how far will the runner