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Chapter 2: Problem 59

Use metric conversion factors to solve each of the following problems: a. If a student is \(175 \mathrm{~cm}\) tall, how tall is the student in meters? b. A cooler has a volume of \(5000 \mathrm{~mL}\). What is the capacity of the cooler in liters? c. A hummingbird has a mass of \(0.0055 \mathrm{~kg}\). What is the mass, in grams, of the hummingbird? d. A balloon has a volume of \(3500 \mathrm{~cm}^{3}\). What is the volume in liters?

Short Answer

Expert verified
a. 1.75 meters, b. 5 liters, c. 5.5 grams, d. 3.5 liters

Step by step solution

01

Convert centimeters to meters

To convert from centimeters to meters, use the conversion factor: 1 meter = 100 centimeters. Therefore, divide the height in centimeters by 100. \[ 175 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 1.75 \text{ m} \]
02

Convert milliliters to liters

To convert from milliliters to liters, use the conversion factor: 1 liter = 1000 milliliters. Therefore, divide the volume in milliliters by 1000. \[ 5000 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 5 \text{ L} \]
03

Convert kilograms to grams

To convert from kilograms to grams, use the conversion factor: 1 kilogram = 1000 grams. Therefore, multiply the mass in kilograms by 1000. \[ 0.0055 \text{ kg} \times 1000 \text{ g/kg} = 5.5 \text{ g} \]
04

Convert cubic centimeters to liters

To convert from cubic centimeters to liters, use the conversion factor: 1 liter = 1000 cubic centimeters. Therefore, divide the volume in cubic centimeters by 1000. \[ 3500 \text{ cm}^3 \times \frac{1 \text{ L}}{1000 \text{ cm}^3} = 3.5 \text{ L} \]

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Key Concepts

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

metric system
The metric system is a decimal-based system of measurement used around the world. It makes scientific calculations simpler because everything is in multiples of ten. It includes units like meters for length, liters for volume, and grams for mass.
For example, in this exercise, we use centimeters, meters, milliliters, liters, kilograms, grams, and cubic centimeters. Each of these units can easily be converted into another by shifting the decimal point.
unit conversion
Unit conversion is the process of changing a value expressed in one type of unit to another type of unit. This is essential in science, especially chemistry, to ensure that measurements are consistent.
For instance, converting 175 cm to meters involves recognizing that 1 meter equals 100 cm. To make the conversion, you divide 175 by 100 to get 1.75 meters. This method holds for converting any metric units: just determine the relationships and move the decimal point accordingly.
dimensional analysis
Dimensional analysis, also known as the factor-label method, is a technique used to convert units. It involves multiplying the quantity by a conversion factor that cancels out the units we want to change.
For example, in converting 0.0055 kg to grams, we multiply by the conversion factor, 1000 g/kg. This cancels the 'kg' unit and converts the value to grams, giving us 5.5 grams. The key is to use conversion factors correctly to keep the units consistent.
volume conversions
Volume conversions change measurements from one volume unit to another. In the metric system, common units of volume are milliliters (mL), liters (L), and cubic centimeters (cm鲁).
For instance, converting 5000 mL to liters involves dividing by the conversion factor, which is 1000 mL per liter. So, you get 5 liters. Similarly, converting cubic centimeters to liters uses the same factor, as 1 cm鲁 equals 1 mL. This means 3500 cm鲁 converts to 3.5 liters.
mass conversions
Mass conversions change measurements from one mass unit to another. In the metric system, common units of mass are kilograms (kg) and grams (g).
For example, converting 0.0055 kg to grams involves using the conversion factor, which is 1000 grams per kilogram. By multiplying 0.0055 kg by 1000, we get 5.5 grams. Understanding these conversion factors helps make sure the values are accurate and compatible in scientific calculations.

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Most popular questions from this chapter

Complete each of the following metric relationships: a. \(1 \mathrm{Mg}=\) _____ \(\mathrm{g}\) b. \(1 \mathrm{~mL}=\) ______ \(\mu \mathrm{L}\) c. \(1 \mathrm{~g}=\) _____ \(\mathrm{kg}\) d. \(1 \mathrm{~g}=\) __________ \(\mathrm{mg}\)

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. The label on a bottle reads \(10 \mathrm{mg}\) of furosemide per \(1 \mathrm{~mL}\) b. The Daily Value (DV) for selenium is 70. mcg. c. An IV of normal saline solution has a flow rate of \(85 \mathrm{~mL}\) per hour. d. One capsule of fish oil contains \(360 \mathrm{mg}\) of omega- 3 fatty acids.

What is the density \((\mathrm{g} / \mathrm{mL})\) of each of the following samples? a. An ebony carving has a mass of \(275 \mathrm{~g}\) and a volume of \(207 \mathrm{~cm}^{3}\) b. \(\quad\) A \(14.3-\mathrm{cm}^{3}\) sample of tin has a mass of \(0.104 \mathrm{~kg}\). c. A bottle of acetone (fingernail polish remover) contains \(55.0 \mathrm{~mL}\) of acetone with a mass of \(43.5 \mathrm{~g}\).

On a typical day, medical personnel may encounter several situations involving measurement. State the name and type of measurement indicated by the units in each of the following: a. During open-heart surgery, the temperature of a patient is lowered to \(29^{\circ} \mathrm{C}\) b. The circulation time of a red blood cell through the body is \(20 \mathrm{~s}\) c. A patient with a persistent cough is given \(10 . \mathrm{mL}\) of cough syrup. d. The amount of iron in the red blood cells of the body is \(2.5 \mathrm{~g}\).

Why can two conversion factors be written for an equality such as \(1 \mathrm{~m}=100 \mathrm{~cm} ?\)
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