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# UM CHEM 1110 - Numbers, Units, & Conversions KEY

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Chemistry 1110 Numbers, Units, & Conversions I. Convert each of the following to scientific notation or to ‘normal’ notation. 93,000,000 9.3x107 0.3841 3.841x10-1 0.00000007241 7.241x10-8 0.005219 5.219x10-3 6184538 6.184538x106 1.393x105 139300 0.00321x104 32.1 5.892x10-3 0.005892 4.9x10-8 0.000000049 9.43x106 9430000 II. Answer each of the following questions based on unit conversions. What power of 10 corresponds to each of the following metric system prefixes? Centi 10-2 Mega 106 Giga 109 Tera 1012 Milli 10-3 Micro 10-6 The hepatitis virus is 45 nm in diameter. How big is this in meters? nano = 1x10-9, therefore 45 nm = 45x10-9 m, or 4.5x10-8 m A typical dose of clonidine for children is approximately 0.0000013 g clonidine/kg body weight. What would be a more convenient way to express this value using SI prefixes? 0.000013 g = 1.3x10-6 g micro = 1x10-6, therefore 1.3 mcg clonidine is more convenient. III. Perform the following conversions using Dimensional Analysis. Be sure to clearly set up appropriate conversion factors in each case! 150 lb to kg 1 kg = 2.205 lb 150 lb * 1 kg2.205 lb = 68.0 kg 26.2 mi to km 1 mi = 1609 m 26.2 mi *1609 m1 mi * 1 km1000 m = 42.2 km 7 ft 2 in to cm 1 in = 2.54 cm 7 ft * 12 in1 ft = 84 in + 2 in = 86 in total 86 in * 2.54 cm1 in = 218.4 cm 14.4 mcL to mL 14.4 mcL *1x10-6 L1 mcL * 1x103 mL1 L = 1.44x10-2 mL or 0.0144 mLIV. Perform each of the following conversions by using Dimensional Analysis. A doctor orders a patient to take 100 mg persantine (a blood thinner) daily. The available formulation is 25 mg persantine/tablet. How many tablets should be given daily? 25 mg persantine = 1 tablet 1 day = 100 mg persantine 100 mg persantine1 day * 1 tablet25 mg persantine = 4 tablets/day Polycyllin is available as a solution containing 250 mg/5 mL. How many mL would you administer to give a dose of 400 mg polycyllin? 250 mg polycyllin = 5 mL 400 mg = 1 dose 400 mg polycyllin1 dose * 5 mL solution250 mg polycyllin = 8 mL solution/dose In a typical person, the level of glucose is about 85 mg/100 mL of blood. If the average body contains about 5.5 L of blood, how many grams of glucose are present in the blood of a typical person? 85 mg glucose100 mL blood * 1000 mL blood1 L blood * 5.5 L blood = 4675 mg glucose 4645 mg glucose * 1x10-3 g glucose1 mg glucose = 4.675 g glucose Drug dosages are often given as mass of drug per body mass, for instance mg/kg or mcg/kg. What is the daily dosage in milligrams per kilogram of body weight for a child weighing 23 kg who takes 2 qty 50 mg tablets of gentamycin? 2 tablets gentamycin * 50 mg gentamycin1 tablet gentamycin * 23 kg body mass = 4.35 mg/kg How many 100 mg tablets of gentamycin should be administered to a 140 lb woman to achieve the same drug dosage? 140 lb body mass * 1 kg body mass2.205 lb body mass * 4.35 mg gentamycin1 kg body mass * 1 tablet100 mg gentamycin = 2.8 tablets A doctor orders a 50 lb child to take 75 mg garamycin every 8 hours. How does this amount compare to the recommended dosage of 2.0-2.5 mg/kg administered every 8 hours for patients with normal renal function? 75 mg garamycin 50 lb * 2.205 lb1 kg = 3.31 mg/kg EXCEEDS RECOMMENDED

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