Part 4- Dimensional Analysis An equality tells a measurement in two different units. Examples: a) 1 inch = 2.54 centimeters b) 39.1 inches = 1 meter c) 1000 mL = 1L To write a conversion factor, you express an equality as a fraction. There are two conversion factors for every equality. Example: equality ... 1 inch = 2.54 cm 1 in 2.54 cm Conversion factors ..... 2.54 cm 1 in Sample Problem: How many quarts is in 2.7 cups? To convert from one unit to the other, follow these steps: 1) Write down the original number given in the problem 2.7 cups 2) Find the equality that converts the given unit to the need unit 4 cups = 1 qt 3) Write the 2 conversion factors for the equality from #2. 4 cups 1 qt 1 qt '4 cups 4) Choose the equality that has your original unit on the bottom and the needed unit on top. 1 qt 4 cups 5) Multiply your original number by the conversion factor chosen in #4.2.7 cups x 1 qt (4 cups = 0.675qt To round the answer, never use the conversion factor. Go by the number your originally started with. 2.7 has 2 significant figures, so your final answer needs to be rounded to 2 significant figures. Final answer = 0.68 qt If you do not know a direct conversion to go from the given unit to the needed unit, then you can use multiple equalities and conversion factors to go from one unit to the other. Example: How many decimeters are in 18 ml I know there are 1000 ml = 1 L and 10 dL = 1L 18 ml X 1 L = 0.018 L 1000 mb 0.018 4 X- 10 dL = 0.18 L 1 L Use the following table to answer the questions below. Show your legible handwritten work which includes equalities and how you multiplied by a conversion factor to get your answers to receive full credit. Round all answers to the correct number of significant figures. TABLE 2.7 Some Common Equalities Quantity Metric (SI) U.S Metric-U.S. Length 1 km = 1000 m 1 ft = 12 in. 2.54 cm = 1 in. (exact) 1 m = 1000 mm 1 yd = 3 ft 1 m = 39.4 in. 1 cm = 10 mm 1 mi = 5280 ft 1 km = 0.621 mi Volume 1 L = 1000 mL 1 qt = 4 cups 946 mL = 1 q 1 dL = 100 ml 1 qt = 2 p 1 L = 1.06 qt 1 mL 1 cm3 1 gal = 4 qt 473 mL = 1 pt 1 mL = 1 cc* 5 mL = 1 t (tsp)* 15 mL = 1 T (tbsp)* Mass 1 kg = 1000 g 1 1b = 16 oz 1 kg = 2.20 lb 1 g = 1000 mg 454 g = 1 1b 1 mg = 1000 mcg* Time 1 h = 60 min 1 h = 60 min 1 min = 60 s 1 min = 60 s "Used in medicine.. Apencilis 12.2 in long. What is its length in cm? . A person has a mass of 72.4 kg. What is that weight in pounds? . How many pints of plasma are present in 5.0 Liters? . For the measurements in Part 3 (the graduated cylinders), convert your each ml- measurement to pints. Cylinder A Cylinder B Cylinder C Cylinder D . For the measurements in Part 3 (the graduated cylinders), convert your each mil- measurement to gallons. Cylinder A Cylinder B Cylinder C Cylinder D