Problem 18 - Chemistry for Allied Health

Question

What is the conversion factor between each pair of units? a. feet and inches b. \(\mathrm{mL}\) and \(\mathrm{cm}^{3}\) c. \(\mathrm{kg}\) and \(\mathrm{g}\) d. cm and m e. \(\mathrm{mm}\) and \(\mathrm{cm}\) \(\mathrm{f}\). inches and centimeters g. grams and pounds h. \(g\) and \(\mu\) g (mcg)

Step-by-Step Solution

Answer

a. 12, b. 1, c. 1000, d. 0.01, e. 0.1, f. 2.54, g. 0.00220462, h. 1,000,000.

Step 1: Feet to Inches

There are 12 inches in a foot. Therefore, the conversion factor from feet to inches is 12. If you have a certain number of feet and want to convert it to inches, you multiply by 12.

Step 2: Milliliters to Cubic Centimeters

1 milliliter is equal to 1 cubic centimeter. Therefore, the conversion factor between milliliters and cubic centimeters is 1.

Step 3: Kilograms to Grams

There are 1000 grams in a kilogram. Thus, the conversion factor from kilograms to grams is 1000. To convert kilograms to grams, you multiply by 1000.

Step 4: Centimeters to Meters

There are 100 centimeters in a meter. The conversion factor from centimeters to meters is 1/100, because 1 cm equals 0.01 meters.

Step 5: Millimeters to Centimeters

There are 10 millimeters in a centimeter. The conversion factor from millimeters to centimeters is 1/10, since 1 mm equals 0.1 cm.

Step 6: Inches to Centimeters

1 inch is equal to 2.54 centimeters. Therefore, the conversion factor from inches to centimeters is 2.54.

Step 7: Grams to Pounds

There are approximately 0.00220462 pounds in a gram. Therefore, the conversion factor from grams to pounds is about 0.00220462.

Step 8: Grams to Micrograms

There are 1,000,000 micrograms (mcg) in a gram. Thus, the conversion factor from grams to micrograms is 1,000,000.

Key Concepts

Conversion Factors

Understanding conversion factors is crucial in unit conversion. A conversion factor is simply a ratio or fraction that is used to convert a quantity expressed in one kind of unit to another. For example, if you want to convert from feet to inches, the conversion factor is 12 because there are 12 inches in one foot. You multiply the number of feet by this factor to get the corresponding number of inches.

Conversion factors are unique for each pair of units, and knowing them helps in transforming measurements accurately without changing the actual size or magnitude of what you are measuring.

Here are some typical conversion factors you should be familiar with:

• Feet to inches: 12
• Kilograms to grams: 1000
• Centimeters to meters: 1/100
• Milliliters to cubic centimeters: 1

By applying the correct conversion factor, you ensure that your calculations are precise and meaningful.

Metric System

The metric system is a widely used system of measurement based on powers of ten. It's used globally because of its simplicity and ease of conversions. Every unit in the metric system is derived from a set of base units, such as the meter for length and the gram for mass.

One of the key features of the metric system is its reliance on standard prefixes to indicate multiples or fractions of units. Here are some examples:

• Kilo- (k): Represents a multiplier of 1000. For example, 1 kilogram (kg) is 1000 grams (g).
• Centi- (c): Represents a hundredth of a unit. For instance, 1 centimeter (cm) is 0.01 meters (m).
• Milli- (m): Represents a thousandth of a unit. For example, 1 millimeter (mm) is 0.001 meters (m).

These prefixes make it easy to convert between larger and smaller units, ensuring convenience in scientific and everyday calculations.

Measurement Units

Measurement units are the standardized quantities used to express physical quantities. They allow us to understand, compare, and communicate measurements accurately. Different systems of measurement exist, but the metric system is one of the most commonly used globally.

Common units you'll encounter include:

• Length: meters (m), centimeters (cm), millimeters (mm)
• Volume: liters (L), milliliters (mL), cubic centimeters ( cm^3 )
• Mass: grams (g), kilograms (kg), micrograms ( μg )

Selecting the proper measurement unit is crucial in ensuring clarity and consistency in communication of quantities, whether you're dealing with scientific data or everyday objects.

Dimensional Analysis

Dimensional analysis is a powerful technique in unit conversion that involves the use of conversion factors to express quantities in different units. It's often used in chemistry and physics to solve problems systematically by canceling out units until the desired unit is obtained.

To perform dimensional analysis: 1. Start with the original value and its unit. 2. Identify the conversion factors needed. 3. Multiply the original value by the appropriate conversion factors. 4. Ensure the units you want to cancel out properly do so.

For example, if you need to convert 5 feet to inches, start with 5 feet and multiply by the conversion factor (12 inches per foot), yielding 60 inches. By arranging the units to cancel out, dimensional analysis provides an organized framework for solving conversion problems, which reduces errors and enhances understanding.