Using Units in Calculations Conversions in Calculations Dimensional

Using Units in Calculations, Conversions in Calculations (Dimensional Analysis)

Using Units in Calculations • Addition and subtraction: units don't change 2 kg + 3 kg = 5 kg 412 m - 12 m = 400 m • This means the units MUST BE THE SAME before adding or subtracting! 3. 001 kg + 112 g = 3. 001 kg + 0. 112 kg = 3. 113 kg 4. 314 m - 2 mm = 4314 mm - 2 mm 4312 mm = 4. 312 m =

Using Units in Calculations •

Conversions Among Units You are used to many basic conversions: • Inches to centimeters • Pounds to kilograms • Degrees Fahrenheit to degrees Celsius But what if you didn’t have your handy phone to look up a conversion program? ? We use CONVERSION FACTORS (and so do conversion programs) to make conversions among units, like 2. 54 cm = 1 inch 2. 2 lbs = 1 kg

Sample Conversions •

Conversion Factors • 5 step plan for converting units 1. 2. 3. 4. 5. identify the unknown, including units choose a starting point list the connecting conversion factors multiply the starting measurement by conversion factors Check the result: does the answer make sense?

More Complicated Conversions • Did you ever wonder how many miles are in a light year? (A light year is the distance light travels in a year. Scientists measure distances to stars in light years. ) • Distance is speed multiplied by time. Light travels at 3. 0 x 108 meters/sec. A year is 365. 25 days long. A mile is 1. 6 km. • We use these and other conversion factors to answer this question.

More Complicated Conversions •

Homework (due Friday 8/21) (20 points) Convert the following. Show all work for credit. 1) 1, 000 min = ? years 2) 92, 000 mg = ? pounds 3) 75 miles/hour = ? meters/sec 4) 8. 3 square yards = ? square cm (i. e. , cm 2)