1Circuit VariablesAssessment ProblemsAP 1.1Use a product of ratios to convert two-thirds the speed of light from metersper second to miles per second:(23)3×108m1 s·100 cm1 m·1 in2.54 cm·1 ft12 in·1 mile5280 feet = 124,274.24 miles1 sNow set up a proportion to determine how long it takes this signal to travel1100 miles:124,274.24 miles1 s= 1100 milesxsTherefore,x=1100124,274.24 = 0.00885 = 8.85×10−3s = 8.85 msAP 1.2To solve this problem we use a product of ratios to change units fromdollars/year to dollars/millisecond. We begin by expressing $10 billion inscientific notation:$100 billion = $100×109Now we determine the number of milliseconds in one year, again using aproduct of ratios:1 year365.25 days·1 day24 hours·1 hour60 mins·1 min60 secs·1 sec1000 ms =1 year31.5576×109msNow we can convert from dollars/year to dollars/millisecond, again with aproduct of ratios:$100×1091 year·1 year31.5576×109ms =10031.5576 = $3.17/ms1–1
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