Question

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the con- version factors needed to convert (a) mm to nm, (b) mg to kg, (c) km to ft, (d) in. \(^{3}\) to \(\mathrm{cm}^{3} .\)

Short answer

(a) To convert mm to nm, multiply the value in mm by 1,000,000. (b) To convert mg to kg, multiply the value in mg by 0.000001. (c) To convert km to ft, multiply the value in km by 1000 and then multiply the result by 3.28084. (d) To convert in³ to cm³, multiply the value in in³ by 16.3871.

Step-by-step solution

(a) Convert mm to nm

To convert millimeters to nanometers, we need to use the following conversion factor: 1 mm = 1,000,000 nm. Thus, to convert a given value in millimeters to nanometers, we simply multiply the value in mm by 1,000,000.

(b) Convert mg to kg

To convert milligrams to kilograms, we will use the conversion factor 1 mg = 0.000001 kg (or equivalently, 1 kg = 1,000,000 mg). Thus, to convert a given value in milligrams to kilograms, we simply multiply the value in mg by 0.000001.

(c) Convert km to ft

To convert kilometers to feet, we need to use two conversion factors: 1 km = 1000 m and 1 m = 3.28084 ft. First, we will convert the given value in kilometers to meters, then convert the value in meters to feet. Thus, to convert a given value in kilometers to feet, we multiply the value in km by 1000, and then multiply the result by 3.28084.

(d) Convert in³ to cm³

To convert cubic inches to cubic centimeters, we need to use the conversion factor 1 in³ = 16.3871 cm³. Thus, to convert a given value in cubic inches to cubic centimeters, we simply multiply the value in in³ by 16.3871.

Key concepts

Metric Units

Metric units form a part of the International System of Units (SI), which is the most widely used system for measurement worldwide. The system is based on 10s, meaning each unit increases by a factor of ten, making conversions relatively straightforward.
Here are a few key points about metric units:

• Length is measured in meters (m).
• Mass is measured in grams (g).
• Volume is measured in liters (L).

When dealing with metric units, understanding prefixes like milli- (1/1,000), centi- (1/100), and kilo- (1,000) is crucial.
For instance, converting millimeters (mm) to nanometers (nm) involves the use of conversion factors based on these prefixes. Since 1 mm equals 1,000,000 nm, this illustrates the ease of multiplying in increments of ten to switch between metric units.

English Units

English units, often referred to as the imperial system, are primarily used in the United States. Unlike the metric system, English units do not use a base-10 system, which can make conversions a bit more challenging.
Here are some principal English units:

• Length is measured in inches (in), feet (ft), and miles (mi).
• Mass is measured in ounces (oz) and pounds (lb).
• Volume is measured in ounces (oz) and gallons (gal).

Getting familiar with specific conversion factors is vital in this system. For example, converting kilometers (which is a metric unit) to feet involves understanding that 1 km equals approximately 3280.84 feet. This can require memorizing specific conversion numbers rather than using a decimal-based system like in metric conversions.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to an equivalent quantity in another set. It ensures that measurements can be consistently reported and understood across different systems.
Here is a general approach to unit conversion:

• Identify the appropriate conversion factor(s).
• Multiply (or divide) the original measurement by these factors to get the equivalent in the new units.
• Check your work to ensure everything makes logical sense in the new measurement context.

Using the original exercise as an example, converting cubic inches to cubic centimeters involves knowing that 1 in³ equals 16.3871 cm³. A precise understanding of these conversion factors allows for seamless conversions, providing clear communication in scientific and daily contexts.