Dimensional Analysis Conversion Factors Dimensional Analysis Lots of

Dimensional Analysis • Conversion Factors • Dimensional Analysis • Lots of Practice

A. Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: Factors: 1 in. = 2. 54 cm 1 in. 2. 54 cm and 2. 54 cm 1 in.

A. Conversion Factors Ø If you know ONE conversion for each w Mass: type of measurement, you w Length: can convert anything! w Volume: Ø You must memorize and use these conversions 454 grams = 1 lb 2. 2 lbs = 1 kg 2. 54 cm = 1 inch 1 mile = 1. 609 km 1 L = 1. 06 quarts 1 L = 1000 m. L 1 L = 1 dm 3 1 m. L = 1 cm 3

A. Conversion Factors Write conversion factors that relate each of the following pairs of units: 1. Liters and m. L 2. Hours and minutes 3. Meters and kilometers

1. Liters and m. L 1 L and 1000 m. L 1 L = 1000 m. L 1 L 2. hours and minutes 1 hr = 60 min 1 hr and 60 min 1 hr 3. meters and kilometers 1 km = 1000 m 1 km and 1000 m 1 km

B. Dimensional Analysis Ø The “Factor-Label” Method w Units, or “labels” are canceled, or “factored” out

B. Dimensional Analysis Ø Steps: 1. Identify starting & ending units. 2. Write down given/1 3. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. Hit enter ONCE! 4. Check units & answer.

Example How many minutes in 2. 5 hours? Conversion factor 2. 5 hr x 60 min 1 hr = 150 min cancel UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

B. Dimensional Analysis Ø How many milliliters are in 1. 00 quart of milk? qt m. L 1. 00 qt 1 L 1000 m. L 1. 057 qt 1 L = 946 m. L

B. Dimensional Analysis Ø You have 1. 5 pounds of gold. Find its volume in cm 3 if the density of gold is 19. 3 g/cm 3. lb cm 3 1. 5 lb 1 kg 1000 g 1 cm 3 2. 2 lb 1 kg 19. 3 g = 35 cm 3

B. Dimensional Analysis Ø How many liters of water would fill a container that measures 75. 0 in 3? in 3 L 75. 0 in 3 (2. 54 cm)3 (1 in)3 1 L 1000 cm 3 = 1. 23 L

B. Dimensional Analysis Your European hairdresser wants to cut your hair 8. 0 cm shorter. How many inches will he be cutting off? cm in 8. 0 cm 1 in 2. 54 cm = 3. 2 in

B. Dimensional Analysis Eastview football needs 550 cm for a 1 st down. How many yards is this? cm 550 cm yd 1 in 1 ft 1 yd 2. 54 cm 12 in 3 ft = 6. 0 yd

B. Dimensional Analysis A piece of wire is 1. 3 m long. How many 1. 5 -cm pieces can be cut from this wire? cm pieces 1. 3 m 100 cm 1 m 1 piece 1. 5 cm = 86 pieces

Square/Cubic Units Ø Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also! Ø Best way: Square or cube the ENITRE conversion factor Ø Example: Convert 4. 3 cm 3 to mm 3 4. 3 cm 3 ( ) 10 mm 1 cm 3 = 4. 3 cm 3 103 mm 3 13 cm 3 = 4300 mm 3

1000 cm 3 ( ) 1 dm 10 cm 3 = 1 dm 3 So, a dm 3 is the same as a Liter ! A cm 3 is the same as a milliliter.