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. Identify the standard conversion between centimeters and inches: 1 inch is equal to 2.54 centimeters.
2. Write the equality based on the conversion: 1 inch = 2.54 cm.
3. Create the first conversion factor by expressing the equality as a fraction: \( \frac{1 \text{ inch}}{2.54 \text{ cm}} \).
4. Create the second conversion factor by inverting the first conversion factor: \( \frac{2.54 \text{ cm}}{1 \text{ inch}} \).
5. Use these conversion factors to convert between centimeters and inches in any given problem by multiplying the quantity by the appropriate conversion factor.

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. This is essential in chemistry and other sciences to ensure that measurements are consistent and comparable. It often involves multiplication by a conversion factor, which is a ratio that expresses how many of one unit are equivalent to another.

Conversion Factors

Conversion factors are fractions that represent the relationship between two different units. For example, to convert centimeters to inches, the conversion factor is based on the equivalence that 1 inch equals 2.54 centimeters. These factors allow for the systematic conversion of measurements from one unit to another while maintaining the same quantity.

Metric and Imperial Systems

The metric system (centimeters) and the imperial system (inches) are two different systems of measurement. Understanding the differences between these systems is crucial for accurate conversions. The metric system is based on powers of ten, making it easier for calculations, while the imperial system uses various units that do not have a consistent base, requiring specific conversion factors for accurate measurement.