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Chapter 2: Problem 63

Perform each of the following conversions using metric conversion factors: a. \(44.2 \mathrm{~mL}\) to liters b. \(8.65 \mathrm{~m}\) to nanometers c. \(5.2 \times 10^{\mathrm{8}} \mathrm{g}\) to megagrams d. \(0.72 \mathrm{ks}\) to milliseconds

Short Answer

Expert verified
a) 0.0442 L, b) 8.65 x 10^9 nm, c) 520 Mg, d) 720,000 ms

Step by step solution

01

Convert milliliters to liters

To convert milliliters (mL) to liters (L), use the conversion factor: 1 L = 1000 mL. So, divide the number of milliliters by 1000. Calculation: \(44.2 \text{ mL} = \frac{44.2}{1000} \text{ L} = 0.0442 \text{ L}\)
02

Convert meters to nanometers

To convert meters (m) to nanometers (nm), use the conversion factor: 1 m = \(10^9\) nm. So, multiply the number of meters by \(10^9\). Calculation: \(8.65 \text{ m} = 8.65 \times 10^9 \text{ nm} = 8.65 \times 10^9 \text{ nm}\)
03

Convert grams to megagrams

To convert grams (g) to megagrams (Mg), use the conversion factor: 1 Mg = \(10^6\) g. So, divide the number of grams by \(10^6\). Calculation: \(5.2 \times 10^8 \text{ g} = \frac{5.2 \times 10^8}{10^6} \text{ Mg} = 520 \text{ Mg}\)
04

Convert kiloseconds to milliseconds

To convert kiloseconds (ks) to milliseconds (ms), use the conversion factor: 1 ks = \(10^3\) s and 1 s = \(10^3\) ms. So, multiply the number of kiloseconds by \(10^3 \times 10^3 = 10^6\). Calculation: \(0.72 \text{ ks} = 0.72 \times 10^6 \text{ ms} = 720,000 \text{ ms}\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

milliliters to liters
Understanding how to convert milliliters (mL) to liters (L) is important in many fields, especially in cooking, science, and medicine. The metric system is built on powers of ten, making conversions straightforward. Since 1 liter equals 1000 milliliters, you can find how many liters are in a given number of milliliters by dividing by 1000.
For instance, converting 44.2 mL to liters, we use the formula: \[ 44.2 \text{ mL} = \frac{44.2}{1000} \text{ L} = 0.0442 \text{ L} \]
This method works for any amount of milliliters you need to convert to liters. Just remember to divide by 1000!
meters to nanometers
Moving from meters (m) to nanometers (nm) might seem complex, but it's just a matter of understanding powers of ten. One meter is equivalent to one billion (\(10^9 \)) nanometers. This is a huge number, but the conversion is easy once you know the relationship.
Suppose you have 8.65 meters and want to express it in nanometers. You multiply by \(10^9\): \[ 8.65 \text{ m} = 8.65 \times 10^9 \text{ nm} = 8.65 \times 10^9 \text{ nm} \]
This conversion helps in fields like physics and engineering where precise measurements at the nanoscale are essential.
grams to megagrams
When dealing with very large masses, converting grams (g) to megagrams (Mg) becomes useful. A megagram is a million grams (\(10^6\) grams). To convert grams to megagrams, you simply divide by \(10^6\).
For example, to convert \(5.2 \times 10^8 \) grams to megagrams, the calculation would be: \[ 5.2 \times 10^8 \text{ g} = \frac{5.2 \times 10^8}{10^6} \text{ Mg} = 520 \text{ Mg} \]
This conversion can be useful in fields such as logistics and agriculture, where large quantities of materials are often handled.
kiloseconds to milliseconds
Converting kiloseconds (ks) to milliseconds (ms) may sound daunting but follows simple conversion steps. One kilosecond equals 1000 seconds (\(10^3\) seconds), and one second equals 1000 milliseconds (\(10^3\) milliseconds). Thus, one kilosecond equals one million (\(10^6\)) milliseconds.
To convert 0.72 kiloseconds to milliseconds: \[ 0.72 \text{ ks} = 0.72 \times 10^6 \text{ ms} = 720000 \text{ ms} \]
This conversion is useful in scenarios requiring precise time measurements, such as in computing and engineering.

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Most popular questions from this chapter

Using conversion factors, solve each of the following clinical problems: a. The physician has ordered \(1.0 \mathrm{~g}\) of tetracycline to be given every six hours to a patient. If your stock on hand is \(500-\mathrm{mg}\) tablets, how many will you need for one day's treatment? b. An intramuscular medication is given at \(5.00 \mathrm{mg} / \mathrm{kg}\) of body weight. What is the dose for a \(180-\mathrm{lb}\) patient? c. A physician has ordered \(0.50 \mathrm{mg}\) of atropine, intramuscularly. If atropine were available as \(0.10 \mathrm{mg} / \mathrm{mL}\) of solution, how many milliliters would you need to give? d. During surgery, a patient receives \(5.0\) pt of plasma. How many milliliters of plasma were given?

Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following: a. A calcium supplement contains \(630 \mathrm{mg}\) of calcium per tablet. b. The Daily Value (DV) for vitamin \(\mathrm{C}\) is \(60 \mathrm{mg}\). c. The label on a bottle reads \(50 \mathrm{mg}\) of atenolol per tablet. d. A low-dose aspirin contains \(81 \mathrm{mg}\) of aspirin per tablet.

Write the numerical value for each of the following prefixes: a. centi b. tera c. milli d. deci

State the name of the unit and the type of measurement indicated for each of the following quantities: a. \(0.8 \mathrm{~L}\) b. \(3.6 \mathrm{~cm}\) c. \(4 \mathrm{~kg}\) d. \(3.5 \mathrm{~h}\) e. \(373 \mathrm{~K}\)

Identify the exact number(s), if any, in each of the following pairs of numbers: a. 5 pizzas and \(50.0 \mathrm{~g}\) of cheese b. 6 nickels and \(16 \mathrm{~g}\) of nickel c. 3 onions and 3 lb of onions d. 5 miles and 5 cars
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