Write the equality and two conversion factors for each of the following pairs of units:
a. centimeters and inches

Verified step by step guidance

1. Step 1: Understand the relationship between centimeters and inches. The standard conversion factor is that 1 inch is equal to 2.54 centimeters.
2. Step 2: Write the equality based on the relationship: 1 inch = 2.54 cm.
3. Step 3: Create the first conversion factor by expressing the equality as a fraction: \( \frac{1 \text{ inch}}{2.54 \text{ cm}} \). This conversion factor is used to convert centimeters to inches.
4. Step 4: Create the second conversion factor by inverting the fraction: \( \frac{2.54 \text{ cm}}{1 \text{ inch}} \). This conversion factor is used to convert inches to centimeters.
5. Step 5: Verify that both conversion factors are consistent with the equality and can be used interchangeably depending on the direction of the conversion.

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to an equivalent quantity in another unit. This is essential in fields like science and engineering, where measurements need to be consistent. Understanding the relationship between different units allows for accurate calculations and comparisons.

Conversion Factors

A conversion factor is a numerical factor used to multiply or divide a quantity when converting from one unit to another. It is derived from the equivalence between the two units. For example, to convert centimeters to inches, the conversion factor is 1 inch = 2.54 centimeters, which can be used to facilitate the conversion.

Metric and Imperial Systems

The metric system and the imperial system are two different systems of measurement. The metric system is based on powers of ten and includes units like meters and liters, while the imperial system includes units like inches and gallons. Understanding these systems is crucial for performing conversions accurately, especially in international contexts.