Which of the following is a valid conversion factor?
$\frac{1 cm^3}{1 L}$
$\frac{1 mL}{100 L}$
$\frac{10 m}{1 dm }$
$\frac{100 cm}{1 m}$
Answer (1)
Check each conversion factor for validity.
1 L 1 c m 3 is incorrect because 1 L = 1000 c m 3 .
100 L 1 m L is incorrect because 100 L = 100000 m L .
1 d m 10 m is incorrect because 10 m = 100 d m .
1 m 100 c m is correct because 1 m = 100 c m .
The valid conversion factor is 1 m 100 c m .
Explanation
Understanding Conversion Factors We are given four conversion factors and we need to determine which one is valid. A conversion factor is a ratio that expresses how many of one unit are equal to another unit.
Analyzing Option 1 Let's analyze each option:
Option 1: 1 L 1 c m 3 We know that 1 L = 1000 c m 3 . Therefore, the correct conversion factor should be 1 L 1000 c m 3 or 1000 c m 3 1 L . So, 1 L 1 c m 3 is not a valid conversion factor.
Analyzing Option 2 Option 2: 100 L 1 m L We know that 1 L = 1000 m L . Therefore, 100 L = 100 × 1000 m L = 100000 m L . The given conversion factor is 100 L 1 m L = 100000 m L 1 m L = 100000 1 , which is not a valid conversion factor.
Analyzing Option 3 Option 3: 1 d m 10 m We know that 1 m = 10 d m . Therefore, 10 m = 10 × 10 d m = 100 d m . The given conversion factor is 1 d m 10 m = 1 d m 100 d m = 100 , which is not a valid conversion factor.
Analyzing Option 4 Option 4: 1 m 100 c m We know that 1 m = 100 c m . Therefore, the given conversion factor 1 m 100 c m is a valid conversion factor because it represents the equality 100 c m = 1 m .
Conclusion Therefore, the valid conversion factor is 1 m 100 c m .
Examples
Conversion factors are essential in everyday life, especially in cooking, construction, and travel. For example, when following a recipe that uses metric units but you only have imperial measuring tools, you need to use conversion factors to adjust the quantities. Similarly, in construction, converting between feet and meters is crucial for accurate building plans. When traveling to a country that uses a different measurement system, understanding conversion factors helps you interpret distances, speeds, and temperatures.
