## Q. 2.12

Solving Unit Conversions in the Numerator and Denominator

A prescription medication requires 11.5 mg per kg of body weight. Convert this quantity to the number of grams required per pound of body weight and determine the correct dose (in g) for a 145-lb patient.

## Verified Solution

 SORT Begin by sorting the information in the problem into given and find. You are given the dose of the drug in mg/kg and the weight of the patient in lb. You are asked to find the dose in g/lb and the dose in g for the 145-lb patient. GIVEN: 11.5 $\frac{mg}{kg}$ 145 lb FIND: $\frac{g}{lb}$; dose in g STRATEGIZE The solution map has two parts. In the first part, convert from mg/kg to g/lb. In the second part, use the result from the first part to determine the correct dose for a 145-lb patient. SOLUTION MAP $\frac{mg}{kg} \underset{\frac{10^{-3} g}{mg} } {\longrightarrow } \frac{g}{kg} \underset{\frac{1 kg}{2.205 lb} }{\longrightarrow }\frac{g}{lb}$   $lb\underset{\underset{\overset{\uparrow }{from first part} }{\frac{g}{lb }}}{\longrightarrow }g$ RELATIONSHIPS USED 1 mg = $10^{-3}$ g (from Table 2.2) 1 kg = 2.205 lb (from Table 2.3) SOLVE Follow the solution map to solve the problem. For the first part, begin with 11.5 mg/kg and multiply by the two conversion factors to arrive at the dose in g/lb. Mark the answer to three significant figures to reflect the three significant figures in the least precisely known quantity. For the second part, begin with 145 lb and use the dose obtained in the first part to convert to g. Then round the answer to the correct number of significant figures, which is three. SOLUTION $11.5 \frac{\cancel{mg}}{\cancel{kg}}\times \frac{10^{-3} g}{\cancel{mg}} \times \frac{1 \cancel{kg}}{2.205 lb}= 0.0052\underline{1} 5 \frac{g}{lb}$   $145 \cancel{lb} \times \frac{0.0052 \underline{1}5 g}{\cancel{lb}}$ = 0.75617 g = 0.756 g CHECK Check your answer. Are the units correct? Does the answer make physical sense? The units of the answer are correct, and the value of the answer makes sense. Drug doses can vary over some range, but in many cases they are between 0  and 1 gram.

Table 2.2

 SI Prefix Multipliers Prefix Symbol Meaning Multiplier tera- T trillion 1,000,000,000,000 $(10^{12})$ giga- G billion 1,000,000,000 $(10^{9})$ mega- M million 1,000,000 $(10^{6})$ kilo- k thousand 1,000 $(10^{3})$ hecto- h hundred 100 $10^{2}$ deca- da ten 10 $10^{1}$ deci- d tenth 0.1 $(10^{-1})$ centi- c hundredth 0.01 $(10^{-2})$ milli- m thousandth 0.001 $(10^{-3})$ micro- µ millionth 0.000001 $(10^{-6})$ nano- n billionth 0.000000001 $(10^{-9})$ pico- p trillionth 0.000000000001 $(10^{-12})$ femto- f quadrillionth 0.000000000000001 $(10^{-15})$

Table 2.3

 Some Common Units and Their Equivalents Length 1 kilometer (km) = 0.6214 mile (mi) 1 meter (m) = 39.37 inches (in.) = 1.094 yards (yd) 1 foot (ft) = 30.48 centimeters (cm) 1 inch (in.) = 2.54 centimeters (cm) (exact) Mass 1 kilogram (kg) = 2.205 pounds (lb) 1 pound (lb) = 453.59 grams (g) 1 ounce (oz) = 28.35 grams (g) Volume 1 liter (L) = 1000 milliliters (mL) = 1000 cubic centimeters $(cm^3)$ 1 liter (L) = 1.057 quarts (qt) 1 U.S. gallon (gal) = 3.785 liters (L)