# Dimensional Analysis Units weve got units weve got

• Slides: 15

Dimensional Analysis Units, we’ve got units, we’ve got bags and bags of units

Dear teacher, would you be so kind To fill our request and use the units we like best! I am a metric woman Living on a standard plan King John has been gone For near a thousand years man, Can’t our units make sense And be decimal events?

Dimensional Analysis is not for everyone. But it's probably for you. First of all then, who should avoid Dimensional Analysis (DA)?

Reasons for not using Dimensional Analysis: 1. You're super-intelligent & enjoy solving relatively simple problems in the most complex manner. 2. You're tired of always getting the correct answers. 3. You're an arty type & you can't be confined by the structure of DA. You like messy solutions scribbled all over the page in every which direction. It's not that you want to make a mistake. But you really don't care that much about the answer. You just like the abstract design created by the free-wheeling solution. . . & the freedom from being confined by structure. 4. You have no interest in going to the prom or making the soccer team, & you don't mind being unpopular, unattractive, ignorant, insecure, uninformed, & unpleasant. http: //www. chemistrycoach. com/use. htm

What are we learning? • How to change from one unit to another for measurements of – Length – Weight – Volume – Temperature • How to change from one unit of rate to another.

Scientists generally work in metric units. Common prefixes used are the following: Prefix Abbr. Meaning Example Mega - M 106 1 megameter = 1 x 106 meters Kilo - k 103 1 kilometer = 1 x 103 meters Centi - c 10 -2 1 centimeter = 1 x 10 -2 meters Milli - m 10 -3 1 millimeter = 1 x 10 -3 meters Micro- µ 10 -6 1 micrometer = 1 x 10 -6 meters Nano- n 10 -9 1 nanometer = 1 x 10 -9 meters

Basic metric units • Length - meter • Weight - gram • Volume - liter

Americans generally work in standard units. Common units for length are the following: Unit Abbr. Example inch in 12 inches = 1 foot ft 3 feet = 1 yard yd 36 inches = 1 yard mile mi 5280 feet = 1 mile 1760 yards = 1 mile

Common standard units for weight are the following: Unit Abbr. Example ounce oz 16 ounces = 1 pound lb 2000 pounds = 1 ton - 32, 000 ounces = 1 ton

Common standard units for volume are the following: Unit Abbr. Example ounce oz 8 ounces = 1 cup - 2 cups = 1 pint pt 2 pints = 1 quart qt 4 quarts = 1 gallon gal 8 pints = 1 gallon

Conversion Factors between Systems • Length: 2. 54 cm = 1 inch • Weight: 1 pound = 453. 6 grams • Volume: 1 quart = 0. 95 liters

Temperature Conversions • Metric units: degrees Celsius (old name centigrade). • Standard Units: degrees Fahrenheit • Conversion Formulas: – F = (9/5)C + 32 – C = (5/9)(F - 32) • Examples – 87 o F = ? o C: C = (5/9)(87 - 32) = (5/9)(55) = 30. 6 o C – 25 o C = ? o. F: F = (9/5)(25) + 32 = 45 + 32 = 77 o F

Example of Conversion: • Change 2500 mm into feet (take to the nearest tenth) – 2500 mm • – = 2500 • = 8. 2 ft.

Follow along with me while I make the following conversions on the board: • • Change 650 miles to centimeters Change 2, 500 grams to pounds. Change 45 liters to gallons. Change 62 o Fahrenheit to degrees Celsius Change 45, 600 mm to miles. Change 99 o Celsius to degrees Fahrenheit. Change 45 pounds to kilograms. Change 75 ounces to quarts.

Converting Rates • Change 75 miles per hour to feet per second. • Change 90 kilometers per hour to feet per second. • Change 144 square feet per second to square meters per minute. • Change 25, 000 meters per second to miles per hour. • Change 55 miles per gallon to kilometers per liter.