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Dimensional Analysis and Metric Conversions SC Standards PS-1.5 Organize and interpret the data from a controlled scientific investigation by using mathematics (including formulas and dimensional analysis), graphs, models, and/or technology. Dimensional Analysis Conversion factors: •using ratios of equivalent values to convert from one unit of measure to another. 1 gram = 1000 milligrams 1g 1000 mg or 1000 mg 1g 60 sec = 1 min. 60 sec 1 min. or 1 min. 60 sec What would the conversion factors be for years and days? 365 days 1 year or 1 year 365 days Dimensional Analysis 1.) Write down given number and unit 2.) Write down “x” and a line 3.) Put given unit on side of line so it will cancel and the desired unit on the other side (may take more than 1 step) 4.) Fill in appropriate numerical relationship for the ratio 5.) Multiply the top and divide by the bottom …see examples… • Example #1 –How many minutes are there in 1 year? 1 year x _______ 365 days x ____ 24 hr x _____ 60 min. 1 year 1 day 1 hr = 525,600 minutes!! Example #2 - How many inches are there in 85.6 cm? (1in = 25.4mm) 10 mm x _____ 1 in 85.6cm x _____ 1 cm 25.4 mm = 33.7 in. Example #3 - How many fluid ounces are there in 2.0 gallons? (1gall = 4 qts, 1 qt = 2 pints, 1 pint = 2 cups, 1 cup = 8 fl. oz.) 4 qts x _____ 2 pt x _____ 1 gal 1 qt. 2 cup x _____ x _____ 8 fl. oz. 1 pt. 1 cup = 256 fl. oz. 2.0 gall Unit Check 1.4 day x 1 day 24 hr Units = day2/hr2 x 60 min 1 hr x 60 sec 1 min Not the final unit needed LecturePLUS Timberlake 11 Learning Check If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet? LecturePLUS Timberlake 12 Solution Initial 8450 ft x 12 in. 1 ft x 1 min 65 m x 2.54 cm 1 in. x 1m 100 cm x 60 sec = 2400 sec 1 min final (2 SF) LecturePLUS Timberlake 13 Compare using <, >, or =. 25) 63 cm 26) 536 cm 6m 53.6 dm 27) 5 g 28) 43 mg 508 mg 5g 29) 1,500 mL 30) 3.6 m 1.5 L 36 cm