Conversion Factors

Algebra-1

1. Fundamental Concepts

Definition: Conversion factors are ratios used to convert quantities from one unit to another within the same measurement system or between different systems.
Dimensional Analysis: A method that uses conversion factors to ensure units cancel out appropriately, leaving the desired unit.
Consistency: Conversion factors must be exact values to maintain accuracy in calculations.

2. Key Concepts

Basic Rule: $1 \text{{m}} = 100 \text{{cm}}$

Dimensionless Ratio: $1 \text{{mile}} = 1.60934 \text{{km}}$

Application: Used to solve problems involving different units of measurement

3. Examples

Example 1 (Basic)

Problem: Convert 5 meters to centimeters.

Step-by-Step Solution:

Use the conversion factor $1 \text{{m}} = 100 \text{{cm}}$ .
Multiply 5 meters by the conversion factor: $5 \text{{m}} \cdot 100 \text{{cm/m}} = 500 \text{{cm}}$ .

Validation: Substitute 5 m → Original: 5; Simplified: 500 cm ✓

Example 2 (Intermediate)

Problem: Convert 2 miles to kilometers.

Step-by-Step Solution:

Use the conversion factor $1 \text{{mile}} = 1.60934 \text{{km}}$ .
Multiply 2 miles by the conversion factor: $2 \text{{miles}} \cdot 1.60934 \text{{km/mile}} = 3.21868 \text{{km}}$ .

Validation: Substitute 2 miles → Original: 2; Simplified: 3.21868 km ✓

4. Problem-Solving Techniques

Labeling Units: Always label units to track conversions and ensure dimensional consistency.
Double-Check Factors: Verify that each conversion factor is correct and appropriate for the problem.
Simplify Ratios: Reduce fractions in conversion factors to their simplest form before performing calculations.