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) \(\mathrm{mm}\) to \(\mathrm{nm}\), (b) \(\mathrm{mg}\) to \(\mathrm{kg}\), (c) \(\mathrm{km}\) to \(\mathrm{ft}\), \((\mathrm{d})\) in. \(^{3}\) to \(\mathrm{cm}^{3}\).

Short answer

(a) To convert mm to nm, multiply the given value by 1,000,000 (1 mm = 1,000,000 nm). \(Value\ in\ mm * 1,000,000 = Value\ in\ nm\). (b) To convert mg to kg, multiply the given value by 0.000001 (1 mg = 0.000001 kg). \(Value\ in\ mg * 0.000001 = Value\ in\ kg\). (c) To convert km to ft, multiply the given value by 3280.84 (1 km = 3280.84 ft). \(Value\ in\ km * 3280.84 = Value\ in\ ft\). (d) To convert in³ to cm³, multiply the given value by 16.3871 (1 in³ = 16.3871 cm³). \(Value\ in\ in^3 * 16.3871 = Value\ in\ cm^3\).

Step-by-step solution

(a) Convert mm to nm

To convert millimeters (mm) to nanometers (nm), we need the conversion factor that relates these two units. We know that 1 millimeter is equal to 1,000,000 nanometers (1 mm = 1,000,000 nm). So, to convert a given value in millimeters to nanometers, we simply multiply the value by the conversion factor: Given value in mm * 1,000,000 = Value in nm.

(b) Convert mg to kg

To convert milligrams (mg) to kilograms (kg), we need the conversion factor that relates these two units. We know that 1 milligram is equal to 0.000001 kilograms (1 mg = 0.000001 kg) or, equivalently, 1 mg = 1 × 10⁻⁶ kg. So, to convert a given value in milligrams to kilograms, we simply multiply the value by the conversion factor: Given value in mg * 0.000001 = Value in kg.

(c) Convert km to ft

To convert kilometers (km) to feet (ft), we need the conversion factor that relates these two units. We know that 1 kilometer is equal to 3280.84 feet (1 km = 3280.84 ft). So, to convert a given value in kilometers to feet, we simply multiply the value by the conversion factor: Given value in km * 3280.84 = Value in ft.

(d) Convert in³ to cm³

To convert cubic inches (in³) to cubic centimeters (cm³), we need the conversion factor that relates these two units. We know that 1 cubic inch is equal to 16.3871 cubic centimeters (1 in³ = 16.3871 cm³). So, to convert a given value in cubic inches to cubic centimeters, we simply multiply the value by the conversion factor: Given value in in³ * 16.3871 = Value in cm³.

Key concepts

Understanding Metric to English Units Conversion

Converting between metric and English units is a fundamental skill in chemistry and various fields of science and engineering. The metric system is a decimal-based system of measurement used worldwide, notable for its ease of use and universal adoption. However, in the United States and a few other countries, English units are more commonly used, making conversions necessary.

For students to successfully convert metric to English units, it's important to familiarize themselves with common conversion factors. These conversion factors are fixed numerical values that allow one to multiply or divide a quantity to switch between units. For example, if we need to convert meters to yards (an English unit), we use the conversion factor 1 meter = 1.09361 yards. Always remember to maintain the units throughout your calculation to ensure accuracy.

Millimeters to Nanometers Conversion

Millimeters (mm) and nanometers (nm) are both units of length in the metric system, which makes this conversion straight forward. To tackle this, you must recognize that 'nano' indicates a factor of 10⁻⁹, while 'milli' represents 10⁻³. Thus, a nanometer is one billionth of a meter, while a millimeter is one thousandth of a meter.

To convert from millimeters to nanometers, you multiply by 1,000,000 (since 1 mm = 1,000,000 nm). For instance, when converting 3 mm to nm, simply do the following calculation: 3 mm * 1,000,000 = 3,000,000 nm.It's a simple multiplication but keep in mind the scale of these units as you're dealing with dimensions that can be quite small on a practical level.

Milligrams to Kilograms Conversion

When dealing with mass, it's common to encounter various units such as milligrams (mg) and kilograms (kg). The prefix 'milli' denotes a thousandth part and 'kilo' denotes a thousand units of the base, which, in this case, is the gram. Therefore, 1 milligram is 0.000001 kilograms (1 mg = 1 × 10⁻⁶ kg).

To convert from milligrams to kilograms, you apply the conversion factor by multiplying the amount in milligrams by 0.000001. For example, to convert 5000 mg to kg, the calculation is:5000 mg * 0.000001 = 0.005 kg.Understanding these prefixes and their relation to the base unit is crucial in chemistry for accurate measurements and calculations.

Kilometers to Feet Conversion

Converting kilometers to feet involves a shift from a metric unit to an English unit. One kilometer is equivalent to 3280.84 feet (1 km = 3280.84 ft). This conversion is handy when measuring distances, such as in land surveying or travel.

To perform this conversion, multiply the value in kilometers by 3280.84. For example, converting 2 kilometers to feet is done by:2 km * 3280.84 = 6561.68 ft.It's important for students to use the correct conversion factor and to understand the context in which they are applying these conversions, as the choice of unit can affect precision and relevance.

Cubic Inches to Cubic Centimeters Conversion

When working with volume, the conversion between cubic inches (in³) and cubic centimeters (cm³) is often required, especially in fields such as chemistry, where volume measurements are essential. There's a straightforward conversion factor here: 1 cubic inch equals 16.3871 cubic centimeters (1 in³ = 16.3871 cm³).

To convert from cubic inches to cubic centimeters, you can multiply the number of cubic inches by 16.3871. For instance, if you want to convert 5 in³ to cm³, you would calculate:5 in³ * 16.3871 = 81.9355 cm³.This type of conversion becomes critical when mixing substances or measuring liquids in different unit systems, so a thorough understanding of volume units and their conversions is indispensable in ensuring accuracy.