Solutions to Physics I H Dimensional Analysis Homework 1.) Convert 7.35 km to: a) meters 103 π = 1 ππ 103 π 7.35 ππ π₯ = 7.35π₯103 π 1 ππ b) centimeters 1 π = 102 ππ 7.35 ππ π₯ 103 π 102 ππ π₯ = 7.35π₯105 ππ 1 ππ 1π c) megameters 106 π = 1 ππ 7.35 ππ π₯ 103 π 1 ππ π₯ = 7.35π₯10β3 ππ 1 ππ 106 π d) picometers 1 π = 1012 ππ 103 π 1012 ππ 7.35 ππ π₯ π₯ = 7.35 π₯1015 ππ 1 ππ 1π 2. Convert 1.750 terabytes to megabytes 1.750 ππ΅ π₯ 106 ππ΅ = 1.750π₯106 ππ΅ 1 ππ΅ 3. Convert 8.62 km/s the mi/h 8.62 ππ 1 ππ 3600 π π₯ π₯ = 19,274 ππ ββ = 1.93π₯105 ππ/β π 1.61 ππ 1β 4. A baby born in the U.S. weighs 3.295 kg according to the scale in the birthing room. Convert this to pounds and ounces so you can tell the grandparents how much the baby weighed. 3.295 ππ π₯ 2.20 ππ = 7.249 ππ 1 ππ 0.249 ππ π₯ 16 ππ§ = 3.984 ππ§ 1 ππ β΄, 3.295 ππ = 7 ππ 3.98 ππ§ 5. A child requires a 5 mL dose of medicine each day. How many days would a gallon of this medicine last? 5 ππΏ 1πΏ 1 πππ π₯ π₯ = 0.0013 πππ βπππ¦ πππ¦ 1000 ππΏ 3.79 πΏ Taking the inverse of this yields: 758 πππ¦π βπππ 6. How many years old are you if you have lived 1 billion seconds? 109 π π₯ 1 βπ 1 πππ¦ 1 π¦πππ π₯ π₯ = 31.7 π¦ππππ 3600 π 24 βπ 365 πππ¦π 7. 1 milliliter of ink can print 50 pages of text. If you had 100 gallons of ink then how many pages could you print? 100 πππ π₯ 3.79 πΏ 1000 ππΏ π₯ = 379,000 ππΏ 1 πππ 1πΏ 379,000 ππΏ π₯ 50 πππππ = 1.9π₯107 πππππ 1 ππΏ 8. A clerk can sort 375 sheets per hour. If there are 225 sheets in an inch, how long will it take her to file 125 inches of loose sheets? 125 ππ π₯ 225 π βπππ‘π = 28,125 π βπππ‘π 1 ππ 28,125 π βπππ‘π π₯ 1 βπ = 75 βππ’ππ 375 π βπππ‘π
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