The factor-label method, also known as dimensional analysis, is a powerful tool for solving problems involving unit conversions. This worksheet provides practice problems with detailed solutions, helping you master this essential chemistry and physics skill. Understanding this method is crucial for success in STEM fields.
What is the Factor-Label Method?
The factor-label method uses conversion factors to cancel out unwanted units and arrive at the desired units. A conversion factor is a fraction where the numerator and denominator represent the same quantity but in different units. For example, since 1 foot = 12 inches, the conversion factors are 1 ft/12 in and 12 in/1 ft. By strategically choosing the correct conversion factor, you can systematically convert between units.
Practice Problems and Solutions
Here are some practice problems demonstrating the factor-label method. Remember to show your work, including canceling units, to ensure accuracy.
Problem 1: Convert 250 centimeters (cm) to meters (m).
Solution:
We know that 1 meter = 100 centimeters. Therefore, our conversion factor is 1 m/100 cm.
250 cm × (1 m/100 cm) = 2.5 m
Answer: 2.5 meters
Problem 2: Convert 5 kilograms (kg) to grams (g).
Solution:
We know that 1 kilogram = 1000 grams. Our conversion factor is 1000 g/1 kg.
5 kg × (1000 g/1 kg) = 5000 g
Answer: 5000 grams
Problem 3: Convert 10000 seconds (s) to hours (hr).
Solution:
We need multiple conversion factors here. We know that 60 seconds = 1 minute and 60 minutes = 1 hour.
10000 s × (1 min/60 s) × (1 hr/60 min) = 10000/3600 hr ≈ 2.78 hr
Answer: Approximately 2.78 hours
Problem 4: Convert 72 miles per hour (mph) to feet per second (ft/s).
Solution:
This problem requires multiple conversion factors: 5280 feet = 1 mile and 3600 seconds = 1 hour.
72 mph × (5280 ft/1 mi) × (1 hr/3600 s) = (72 × 5280)/3600 ft/s = 105.6 ft/s
Answer: 105.6 feet per second
Problem 5: A rectangular prism has dimensions of 15 cm, 20 cm, and 25 cm. Calculate its volume in cubic meters (m³).
Solution:
First, calculate the volume in cubic centimeters: 15 cm × 20 cm × 25 cm = 7500 cm³. Then, convert to cubic meters using the conversion factor (1 m/100 cm)³.
7500 cm³ × (1 m/100 cm)³ = 7500 cm³ × (1 m³/1,000,000 cm³) = 0.0075 m³
Answer: 0.0075 cubic meters
Tips for Success with the Factor-Label Method
- Clearly write out your units: This helps you visualize the cancellation of units.
- Choose the correct conversion factor: Make sure the units cancel appropriately.
- Check your answer: Does the magnitude of the answer make sense?
This worksheet provides a foundation for mastering the factor-label method. Practice regularly, and you'll become proficient in performing unit conversions for various scientific applications. Remember to always double-check your work!
