Problem 54 - 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) \mum to mm, (b) ms to ns, (c) mi to km, (d) \(\mathrm{ft}^{3}\) to \(\mathrm{L}\) .

Step-by-Step Solution

Answer

To convert the given units, we can use the following conversion factors: (a) 1 mm = 1,000 µm, so 1 µm * (1 mm / 1,000 µm). (b) 1 ms = 1,000,000 ns, so 1 ms * (1,000,000 ns / 1 ms). (c) 1 mi = 1.60934 km, so 1 mi * (1.60934 km / 1 mi). (d) 1 ft^3 = 28.3168 L, so 1 ft^3 * (28.3168 L / 1 ft^3).

Step 1: (a) Converting micrometers to millimeters

To convert µm to mm, we need the conversion factor for micrometers and millimeters. We know that: 1 millimeter (mm) = 1,000 micrometers (µm) Now, we can set up the conversion using the given conversion factor: 1 µm * (1 mm / 1,000 µm) The µm unit cancels out, leaving us the converted value in mm.

Step 2: (b) Converting milliseconds to nanoseconds

To convert ms to ns, we'll need the conversion factor for milliseconds and nanoseconds. We know that: 1 millisecond (ms) = 1,000,000 nanoseconds (ns) Now, we can set up the conversion using the given conversion factor: 1 ms * (1,000,000 ns / 1 ms) The ms unit cancels out, leaving us the converted value in ns.

Step 3: (c) Converting miles to kilometers

To convert mi to km, we'll need the conversion factor for miles and kilometers. We know that: 1 mile (mi) = 1.60934 kilometers (km) Now, we can set up the conversion using the given conversion factor: 1 mi * (1.60934 km / 1 mi) The mi unit cancels out, leaving us the converted value in km.

Step 4: (d) Converting cubic feet to liters

To convert ft^3 to L, we'll need the conversion factor for cubic feet and liters. We know that: 1 cubic foot (ft^3) = 28.3168 liters (L) Now, we can set up the conversion using the given conversion factor: 1 ft^3 * (28.3168 L / 1 ft^3) The ft^3 unit cancels out, leaving us the converted value in L.

Key Concepts

Metric System

The Metric System is a uniform way of measuring that is used worldwide due to its simplicity and ease of conversion between different units. It is a decimal-based system, meaning it works in powers of ten. This makes calculations and conversions straightforward. For example, converting micrometers to millimeters is simple because both units are part of the same system. To convert between metric units, there's usually a base conversion factor based on powers of ten:

• 1 kilometer (km) = 1,000 meters (m)
• 1 meter (m) = 1,000 millimeters (mm)
• 1 millimeter (mm) = 1,000 micrometers (µm)

Makes it easy, right? You just move the decimal point to convert between units. When you understand how the metric system is structured, it becomes very intuitive to move from one unit to the next.

SI Units

The SI Units, often called the International System of Units, are an extension of the metric system. This system is universally accepted for scientific and technical use. It comprises base units and derived units that provide a cohesive framework for measurement. The advantage of SI units is their standardization, facilitating global communication in science and industry. Some base units include:

• The meter (m) for distance
• The kilogram (kg) for mass
• The second (s) for time

Derived units, like the liter (L) for volume or the millisecond (ms) for time intervals, are based on these fundamental units, adhering to the consistent logic of the SI system. Using SI units ensures that measurements are precise and reliable, no matter where they are taken or reported.

Conversion Factors

A Conversion Factor is a number used to change one set of units to another, by multiplying or dividing. It allows us to switch between unit systems seamlessly. Each conversion factor is derived from the ratio of two equivalent measurements in different units. For example, converting units requires also setting up a proper equation where units cancel out:

• To convert micrometers (µm) to millimeters (mm), use the factor 1 mm = 1,000 µm.
• For milliseconds (ms) to nanoseconds (ns), the factor is 1 ms = 1,000,000 ns.
• Converting miles to kilometers involves a factor of 1 mi = 1.60934 km.
• From cubic feet (ft³) to liters (L), use 1 ft³ = 28.3168 L.

By applying these conversion factors, you transform quantities from one unit to another accurately. They are essential tools in practical calculations, bridging different unit measurements effectively.