Question 2.7: Capillaries, the microscopic vessels that carry blood from s......
Capillaries, the microscopic vessels that carry blood from small arteries to small veins, are on the average only 1 mm long. What is the average length of a capillary in inches?
Step 1: The given quantity is 1 mm, and the units of the desired quantity are inches.
\quad\quad\quad\quad\quad1 mm = ? in.
Step 2: The conversion factor needed for a one-step solution, millimeters to inches, is not given in Table 2.2. However, a related conversion factor, meters to inches, is given. Therefore, we first convert millimeters to meters and then use the meters-to-inches conversion factor in Table 2.2.
\quad\quad\quad\quad\quadmm → m → in.
The correct conversion factor setup is
\quad\quad\quad\quad\quad 1 \cancel{mm}\times(\frac{10^{-3} \cancel{m}}{1 \cancel{mm}})\times (\frac{39.4 in.}{1.00 \cancel{m}})= ? in.
All of the units except for inches cancel, which is what is needed. The information for the first conversion factor was obtained from the meaning of the prefix milli-.
\quad\quadThis setup illustrates the fact that sometimes the given units must be changed to intermediate units before common conversion factors, such as those found in Table 2.2, are applicable.
Step 3: Collecting the numerical factors and performing the indicated math gives
\quad\quad\quad\quad\quad \left(\frac{1\times10^{-3}\times 39.4}{1\times 1.00}\right) in.= 0.0394 in. \quad\quad (calculator answer)\\\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 0.04 in. \quad\quad (correct answer)
The calculator answer must be rounded to one significant figure because 1 mm, the given quantity, contains only one significant figure.
| TABLE 2.2 Equalities and Conversion Factors That Relate the English and Metric Systems of Measurement | ||
| Metric to English | English to Metric | |
| Length | ||
| 1.00 inch = 2.54 centimeters | \frac{1.00 in.}{2.54 cm} | \frac{2.54 cm}{1.00 in.} |
| 1.00 meter = 39.4 inches | \frac{39.4 in.}{1.00 m} | \frac{1.00 m}{39.4 in.} |
| 1.00 kilometer = 0.621 mile | \frac{0.621 mi}{1.00 km} | \frac{1.00 km}{0.621 mi} |
| Mass | ||
| 1.00 pound = 454 grams | \frac{1.00 lb}{454 g} | \frac{454 g}{1.00 lb} |
| 1.00 kilogram = 2.20 pounds | \frac{2.20 lb}{1.00 kg} | \frac{1.00 kg}{2.20 lb} |
| 1.00 ounce = 28.3 grams | \frac{1.00 oz}{28.3 g} | \frac{28.3 g}{1.00 oz} |
| Volume | ||
| 1.00 quart = 0.946 liter | \frac{1.00 qt}{0.946 L} | \frac{0.946 L}{1.00 qt} |
| 1.00 liter = 0.265 gallon | \frac{0.265 gal}{1.00 L} | \frac{1.00 L}{0.265 gal} |
| 1.00 milliliter = 0.0338 fluid ounce | \frac{0.0338 fl oz}{1.00 mL} | \frac{1.00 mL}{0.0338 fl oz} |