Carry out the following conversions: (e) \$3.99/lb to dollars per kg

Verified step by step guidance

1. Identify the conversion factors needed: 1 lb = 0.453592 kg.
2. Set up the conversion by writing the given value \$3.99/\text{lb}$ and multiply it by the conversion factor to cancel out pounds.
3. The conversion setup will be: \$3.99/\text{lb} \times (1 \text{ lb} / 0.453592 \text{ kg})$.
4. Simplify the expression by canceling out the units of pounds (lb) to leave dollars per kilogram (kg).
5. Perform the division to find the value in dollars per kilogram.

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set of units. This is essential in chemistry and other sciences to ensure that measurements are consistent and comparable. For example, converting pounds to kilograms requires knowing the relationship between these units, specifically that 1 pound is approximately 0.453592 kilograms.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one unit of measurement to another by using conversion factors. It involves multiplying the original measurement by a fraction that represents the relationship between the two units. This method ensures that units cancel appropriately, leading to the desired unit in the final answer, such as converting dollars per pound to dollars per kilogram.

Conversion Factors

Conversion factors are ratios that express how many of one unit are equal to another unit. They are crucial in unit conversions, as they provide the necessary information to switch between different measurement systems. For instance, to convert from pounds to kilograms, the conversion factor is 1 lb = 0.453592 kg, which allows for accurate calculations when changing units.