Practical Dimensional Analysis for Unit Conversions
The concepts of dimensional analysis through visual examples and practice problems. Learn how to choose appropriate conversion factors to convert between units effortlessly. Explore metric conversions and solve real-world scenarios by mastering unit conversion techniques.
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Presentation Transcript
Dimensional Analysis
Unit Conversion Factor A fraction whose numerator and denominator are equivalent (you can also use the reciprocal)
To solve a dimensional analysis problem you want to choose a unit conversion factor that Introduces the unit you want in the answer Cancels out the original unit so that the one you want is all that is left.
Canceling out Words inches miles hours minutes inches feet feet miles = = seconds minutes hours seconds = =
Practice: Choose the appropriate conversion factor. inches 1 12 in. 1 ft 1 ft 12 in. Inches to feet minutes 1 1 hr 60 min 60 min 1 hr Minutes to hours meters 1 1 m 100 cm 100 cm 1 m Meters to centimeters
Prefix Mega- kilo- hecto- BASE UNIT deci- centi- milli- micro- nano- pico- Abbrev M k h g, L, m d c m n p Factor = 1 base unit (0.0000001) 10-6 (0.001) 10-3 (0.01) 10-2 1 101 102 103 (1000000) 106 (1000000000) 109 (1000000000000) 1012 Metric Conversions
Examples One bag of apples weighs 64 ounces. How many pounds does it weigh? 1 lb 64 oz 16 oz 64 1 lb 16 = = = 4 lb Darren drank 2 liters of water. How many milliliters of water did he drink? 1000 mL 2 1000 mL 2 L 1 L = = = 2000 mL 1 L
Convert 80 miles per hour to feet per hour. 80 mi 1 hr 1 mi 5,280 ft 80 5280 ft 1 hr 422,400 ft 1 hr = = = = Convert 63,360 feet per hour to miles per hour. 63,360 ft 1 hr 63,360 ft 1 mi 1 hr 5280 ft 12 mi 1 hr 1 mi 5280 ft = = = =
D.A. Activity #1 Practice in your notebook 1. Convert 38 cm to m 2. Convert 417 mg to g 3. Convert 80 m to km 4. Convert 0.0025L to nL 5. Convert 0.17 m to mm
D.A. Activity #1 Answers D.A. Activity #1 Answers 1. 0.38 m 2. 0.417 g 3. 0.030 km 4. 2,500,000 nL 5. 170 mm
D.A. Activity D.A. Activity #2 #2 1.Convert 97.0 miles to km. 2.Convert 86 L to L. 3.Convert 980 cm to Mm.
1. Convert 97.0 miles to km. 1. Convert 97.0 miles to km. = 156.073 156 km 97.0 mi 1.609 km 1 mi
2 2. Convert 86 L to L. . Convert 86 L to L. 86 L 106 L 1 L = 0.000086 L
3 3. Convert 980 cm to Mm. . Convert 980 cm to Mm. whatttttt whatttttt 980 cm 1 m 10-6 Mm = 0.0000098 Mm 102 cm 1 m 10-6 Mm = 0.0000098 Mm 102 cm 980 cm
A little bit harder now Sheila ran a half-marathon (13.1 miles). She wants to know how many centimeters she ran.
Convert 13.1 miles to cm. Convert 13.1 miles to cm. 102 cm = 2110000 10-3 km 1 m 13.1 mi 1.609 km 1 m cm 1 mi
Mark drank 7.6 ounces of gatorade. He wants to know how many nanoliters he drank. (there are 128 oz in one gallon).
Convert 7.6 ounces to Convert 7.6 ounces to nL nL. . 109 nL = 2.2 x 108 nL 7.6 oz 1 gal 1 L 128 oz 0.264 gal 1 L
