Conversion Factors Dimensional Analysis Lots of Practice
A. Conversion Factors Example: 1 in. = 2.54 cm Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.
A. Conversion Factors If you know ONE conversion for each type of measurement, you can convert anything! You must memorize and use these conversions Mass: 454 grams = 1 lb 2.2 lbs = 1 kg Length: 2.54 cm = 1 inch 1 mile = 1.609 km Volume: 1 L = 1.06 quarts 1 L = 1000 mL 1 L = 1 dm3 1 mL = 1 cm3
A. Conversion Factors 1. Liters and mL 2. Hours and minutes Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers
1. Liters and mL 1 L = 1000 mL 1 L and 1000 mL 1000 mL 1 L 2. hours and minutes 1 hr = 60 min 1 hr and 60 min 60 min 1 hr 3. meters and kilometers 1 km = 1000 m 1 km and 1000 m 1000 m 1 km
B. Dimensional Analysis The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out
B. Dimensional Analysis 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 = 150 min 1 hr cancel UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!
B. Dimensional Analysis How many milliliters are in 1.00 quart of milk? qt mL 1.00 qt 1 L 1.057 qt 1000 mL 1 L = 946 mL
B. Dimensional Analysis You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. lb cm3 1.5 lb 1 kg 2.2 lb 1000 g 1 kg 1 cm3 19.3 g = 35 cm3
B. Dimensional Analysis How many liters of water would fill a container that measures 75.0 in3? in3 L 75.0 in3 (2.54 cm)3 (1 in)3 1 L 1000 cm3 = 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 1st down. How many yards is this? cm yd 550 cm 1 in 2.54 cm 1 ft 12 in 1 yd 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 Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also! Best way: Square or cube the ENITRE conversion factor Example: Convert 4.3 cm3 to mm3 ( ) 4.3 cm3 10 mm 3 1 cm 4.3 cm3 103 mm3 13 cm3 = = 4300 mm3
( ) 1000 cm3 1 dm 3 10 cm = 1 dm3 So, a dm3 is the same as a Liter ! ( ) = 1 dm3 So, a dm3 is the same as a Liter ! A cm3 is the same as a milliliter.