Why can two conversion factors be written for an equality such as 1 m = 100 cm?

Verified step by step guidance

1. Understand that a conversion factor is a ratio used to express a quantity in different units.
2. Recognize that the equality 1 m = 100 cm can be expressed as two different conversion factors: \( \frac{1 \text{ m}}{100 \text{ cm}} \) and \( \frac{100 \text{ cm}}{1 \text{ m}} \).
3. Note that each conversion factor is a fraction that equals 1, allowing you to convert between meters and centimeters without changing the value of a measurement.
4. Use the conversion factor \( \frac{1 \text{ m}}{100 \text{ cm}} \) to convert from centimeters to meters by multiplying the given value in centimeters by this factor.
5. Use the conversion factor \( \frac{100 \text{ cm}}{1 \text{ m}} \) to convert from meters to centimeters by multiplying the given value in meters by this factor.

Key Concepts

Unit Equality

Unit equality refers to the relationship between two different units that represent the same quantity. For example, 1 meter is equal to 100 centimeters, establishing a direct conversion between these two units. This equality allows for the conversion of measurements from one unit to another without changing the actual value of the quantity.

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 unit equalities and can be expressed in two ways. For the equality 1 m = 100 cm, the conversion factors can be written as 100 cm/1 m or 1 m/100 cm, allowing for flexibility in calculations depending on the desired unit.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert between units by using conversion factors. It involves multiplying the quantity by a conversion factor that cancels out the original unit and introduces the desired unit. This method ensures that the final answer is expressed in the correct units, making it a powerful tool in chemistry and other scientific disciplines.