7.4 Dimensional Analysis and Conversions to and from the Metric System 443 MATHEMATICS TODAY Blood Pressure The metric system is used in medicine worldwide. One example is that our prescription drugs are often measured in milligrams ( mg ) or milliliters m( ). A second example is blood pressure readings. Blood pressure typically has two readings, written as a ratio like this: 118 76 mm Hg which is read “118 over 76 millimeters of mercury.” The top number, called systolic pressure , measures the pressure in the arteries when the heart beats (when the heart muscles contract). The bottom number, called diastolic pressure , measures the pressure in the arteries between heart beats (when the heart muscle is resting). According to the American Heart Association, normal blood pressure for adults over 20 years old is considered to be both less than 120 systolic pressure and less than 80 diastolic pressure. Why This Is Important The metric system is used in medical applications in the United States and worldwide. A basic understanding of the metric system is helpful when monitoring one’s health. Researchers around the world use the metric system so they can share information more easily with each other and work together to determine cures for illnesses. Example 7 Organic Fertilizer The label of Poppy’s Pre-Plant organic fertilizer recommends mixing 1 bag of fertilizer with 1.5 gallon of water. This mixture can then be used to fertilize a garden area of 300 square feet. Diep’s rectangular garden is 9 meters long by 6 meters wide. a) Determine the number of liters of water Diep must mix with 1 bag of fertilizer to obtain the recommended mixture. b) How many bags of fertilizer must be purchased to fertilize Diep’s entire garden? Assume only whole bags can be purchased. Solution a) From Table 7.7, we see that = 1 gallon 3.7854 liters. We use this equation to form the unit fraction 3.7854 1 gal and the conversion of 1.5 gallons to liters follows. ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = = ≈ 1.5 gal 3.7854 1gal 1.5(3.7854) 5.6781 5.68 Thus, Diep must mix about 5.68 liters of water to obtain the recommended mixture. b) The recommended mixture can fertilize 300 square feet. We begin by converting this area to square meters. From Table 7.7, we see that 1 square foot 0.0929 square meters. = We use this equation to form the unit fraction 0.0929 m 1 ft 2 2 and the conversion of 300 square feet to square meters follows. ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = = 300 ft 0.0929 m 1 ft 300(0.0929) m 27.87 m 2 2 2 2 2 So, the mixture can cover an area of 27.87 square meters. Next, to determine the area of Diep’s rectangular garden we multiply the length by the width: (9 meters) (6 meters), × or 54 square meters. To determine the number of bags Diep needs to purchase, we divide the area of the garden, 54 square meters, by the area each bag can fertilize, 27.87 square meters. 54 27.87 1.94 ≈ Thus, Diep needs to purchase 2 bags of fertilizer. 7 Now try Exercise 45 Example 8 Determining Dosage by Weight Drug dosage is often administered according to a patient’s weight. For example, 30 mg of the drug vancomycin is to be given for each kilogram of a person’s weight. If Martha, who weighs 136 lb, is to be administered the drug, what dosage should she be given? Solution First we need to convert Martha’s weight into kilograms. From Table 7.7, we see that 1 lb 0.4536 kg. = We obtain our unit fraction from this information. = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ≈ 136 lb 136 lb 0.4536 kg 1 lb 61.69 kg Next, since 30 mg of the drug is to be given for each kilogram of a person’s weight, we multiply 61.69 kg by 30 to determine the dosage. = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ≈ Amount of drug 61.69 kg 30 mg 1 kg 1850.7 mg Thus, 1850.7 mg, or 1.8507 g, of the drug should be given. 7 Now try Exercise 47 Instructor Resources for Section 7.4 in MyLab Math • Objective-Level Videos 7.4 • PowerPoint Lecture Slides 7.4 • MyLab Exercises and Assignments 7.4 • Chapter 7 Projects Shutterstock
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