Problem 44 - Chemistry The Central Science

Question

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (a) \(\mu \mathrm{m}\) to \(\mathrm{mm},\) (b) \(\mathrm{ms}\) to \(\mathrm{ns}\), (c) \(\mathrm{mi}\) to \(\mathrm{km},\) (d) \(\mathrm{ft}^{3}\) to \(\mathrm{L}\)

Step-by-Step Solution

Answer

The conversion factors needed for each conversion are as follows: 1. 1 μm = \( \frac{1}{1000}\) mm 2. 1 ms = 1,000,000 ns 3. 1 mi ≈ 1.60934 km 4. 1 ft³ ≈ 28.3168 L

Step 1: 1. Convert μm to mm

In order to convert micrometers (μm) to millimeters (mm), we need to recall the relationship between them: 1 millimeter (mm) = 1000 micrometers (μm). Therefore, the conversion factor for μm to mm is: 1 μm = \( \frac{1}{1000}\) mm

Step 2: 2. Convert ms to ns

In order to convert milliseconds (ms) to nanoseconds (ns), we need to recall the relationship between them: 1 second (s) = 1000 milliseconds (ms) = 1,000,000,000 nanoseconds (ns). Therefore, the conversion factor for ms to ns is: 1 ms = 1,000,000 ns

Step 3: 3. Convert mi to km

In order to convert miles (mi) to kilometers (km), we need to recall the relationship between them: 1 mile (mi) ≈ 1.60934 kilometers (km). Therefore, the conversion factor for mi to km is: 1 mi ≈ 1.60934 km

Step 4: 4. Convert ft³ to L

In order to convert cubic feet (ft³) to liters (L), we need to recall the relationship between them: 1 cubic foot (ft³) ≈ 28.3168 liters (L). Therefore, the conversion factor for ft³ to L is: 1 ft³ ≈ 28.3168 L

Key Concepts

Metric Units

The metric system is a decimal-based system of measurements used widely around the world. It simplifies calculations and conversions because it uses the base ten numbering system. Common metric units include meters for length, grams for mass, and liters for volume.

Key advantages of using metric units include:

• Simplicity in conversion; simply move the decimal point.
• Uniform prefixes like 'kilo-', 'centi-', and 'milli-' that denote multiples or fractions of ten.
• Global standardization makes scientific communication easier across countries.

Metric units are crucial for ensuring precision in scientific, engineering, and everyday calculations.

English Units

English units, often also known as imperial units, are a system of measurements used mainly in the United States. They differ from the decimal-based metric system and include inches, feet, pounds, and gallons.

Some distinguishing features of English units are:

• The system does not have uniform conversion factors; for example, 12 inches in a foot, 16 ounces in a pound.
• Measurements are often more cumbersome to convert manually.
• Commonly used in everyday U.S. life, such as for road miles, and consumer product measurements.

Despite its complexity, it remains dominant in the U.S. for cultural and practical reasons.

Conversion Factors

Conversion factors are essential tools in both the metric and English systems, utilized to translate one unit of measurement into another. They are crucial for calculations in scientific, engineering, and day-to-day applications.

Understanding conversion factors involves:

• A fixed numerical value that represents the ratio of two units of measurement.
• Allowing transformations even between disparate systems like metric and English, e.g., miles to kilometers.
• Often based on standardized equations, helpful for consistent and accurate calculations.

Mastering conversion factors boosts accuracy and efficiency in various computational applications.

Micrometers to Millimeters

Converting micrometers (μm) to millimeters (mm) involves a simple application of the metric system's base ten structure. The relationship between these two units is 1 millimeter = 1000 micrometers. Therefore, moving the decimal point three places to the left converts μm to mm.

Key steps in the conversion:

• Identify that 1 μm is \(rac{1}{1000}\) mm.
• Perform calculations by dividing given micrometer readings by 1000.
• Provides precision for tasks needing small scale measurements, like in scientific experimentations.

Easily converting micrometers to millimeters is a testament to the elegance of the metric system.

Milliseconds to Nanoseconds

Converting milliseconds (ms) to nanoseconds (ns) is another example of the metric system's simplicity in unit conversion. With 1 second equating to 1,000 milliseconds and also to 1,000,000,000 nanoseconds, the conversion becomes straightforward.

Conversion insights:

• 1 ms equals 1,000,000 ns, underlining the exponential nature of metric units.
• Provides accuracy when dealing with time-sensitive measurements, like in technology and physics.
• Calculating conversions involves multiplying milliseconds by 1,000,000.

Such conversions underline the wide range and precision of the metric system's temporal measurements.

Miles to Kilometers

Miles (mi) to kilometers (km) conversion straddles the English and metric systems. This conversion uses the factor 1 mile = 1.60934 kilometers, which enables the conversion of distances.

To convert, remember to:

• Multiply the number of miles by 1.60934.
• Ensure accuracy for geographical and transportation planning applications.
• Supports global standardization in communication and navigation systems that use kilometers.

This conversion is essential for international travel and scientific research.

Cubic Feet to Liters

Cubic feet to liters is a conversion between the English and metric systems that focuses on volume. The conversion factor is 1 cubic foot = 28.3168 liters, used in various practical applications.

Conversion essentials:

• Multiply the volume in cubic feet by 28.3168 to find its value in liters.
• Provides utility in construction, engineering, and household measurements.
• Promotes consistency and ease when using the metric system's volumetric measures.

Using liters offers a more precise and universal measurement, especially outside the U.S.