Question

State the following metric-English equivalents: (a) ? $\mathrm{cm}=1\mathrm{in}$. (b) $?\mathrm{g}=1\mathrm{lb}$ (c) ? $\mathrm{mL}=1\mathrm{qt}$ (d) ? $\mathrm{s}=1\sec$

Short answer

(a) 2.54 cm/in. (b) 453.592 g/lb (c) 946.353 mL/qt (d) 1 s/second.

Step-by-step solution

Converting Centimeters to Inches

In order to convert centimeters to inches, you need to use the conversion factor between these two units. By definition, 1 inch equals 2.54 centimeters.

Converting Grams to Pounds

To convert grams to pounds, it's important to recognize that 1 pound is equivalent to 453.592 grams.

Converting Milliliters to Quarts

The conversion factor between milliliters and quarts involves knowing that 1 quart is equal to approximately 946.353 milliliters.

Converting Seconds to Seconds (Trivial Conversion)

Seconds and 'sec' are the same time unit. Therefore, this conversion is direct, as 1 second equals 1 second.

Key concepts

Unit Conversion

Unit conversion is a fundamental concept that helps us change a measurement from one unit to another, facilitating communication and understanding between different systems of measurement.
To perform a unit conversion, it's crucial to know the relationship between the units involved. This relationship is often expressed as a "conversion factor," which serves as a bridge to convert any given measure to its equivalent in another unit.
Engaging in unit conversion is essential in various fields, such as science, engineering, and everyday life, where you might need to understand measurements expressed in different units. Let's explore some common conversion factors used in these processes.

• Centimeters to Inches: Use 1 inch = 2.54 centimeters.
• Grams to Pounds: Use 1 pound = 453.592 grams.
• Milliliters to Quarts: Use 1 quart = 946.353 milliliters.
• Seconds to Seconds: Direct conversion, as the units are identical.

Understanding unit conversion involves recognizing these equivalences and applying them as needed to convert measurements accurately.

Conversion Factors

Conversion factors are numerical values used to express the relationship between two different units. They are crucial in the process of unit conversion because they provide the necessary multipliers to change one unit into another.
For example, to convert inches to centimeters, the conversion factor is 2.54. This means you multiply the number of inches by 2.54 to get the equivalent number of centimeters.
Here's how conversion factors work in practice:

• Find the appropriate conversion factor for the units you are converting.
• Multiply or divide by the conversion factor, depending on whether you are converting from a smaller unit to a larger unit or vice versa.
• Always keep track of the units during the calculation to ensure accuracy.

Mastering the use of conversion factors makes it easier to handle problems that require working with different measurement systems, ensuring that you get correct and meaningful results.

Metric System

The metric system is a decimal-based system of measurement used by most of the world. It provides a standardized way to measure length, mass, volume, and other quantities.
Some of the main units of the metric system include:

• Meter (m) for length
• Gram (g) for mass
• Liter (L) for volume
• Second (s) for time

The metric system is incredibly user-friendly because it is based on powers of ten. This means converting between different metric units, such as from meters to kilometers, is often just a matter of moving the decimal point.
For example:

• 1 kilometer (km) = 1,000 meters (m)
• 1 gram (g) = 0.001 kilograms (kg)
• 1 milliliter (mL) = 0.001 liters (L)

The ease of scaling within the metric system simplifies calculations, making it a preferred choice in scientific and international contexts.

English Measurement System

The English measurement system, also known as the Imperial system, is used primarily in the United States and a few other countries. This system includes units such as inches, feet, pounds, and quarts.
In contrast to the metric system, the English system is not based on a simple decimal structure, which can make conversions more complex. Here are some common units in the English measurement system:

• Inch (in) for length
• Pound (lb) for weight
• Quart (qt) for volume
• Second (sec) for time

Some common conversions within this system include:

• 12 inches = 1 foot
• 3 feet = 1 yard
• 16 ounces = 1 pound
• 4 quarts = 1 gallon

Converting units within the English system often requires memorizing various conversion factors, making it less intuitive than the metric system. However, it remains a widely used system for various applications, particularly in the United States.