Show the proper setup for the problem. What is Paul’s height in feet? 185 cm \times \frac{\text{ft}}{\text{cm}} = \text{ft}
The Correct Answer and Explanation is:
To properly convert Paul’s height from centimeters to feet, we follow a two-step process using standard unit conversion factors:
Proper Setup:
185 cm×(1 inch2.54 cm)×(1 foot12 inches)=feet185\ \text{cm} \times \left(\frac{1\ \text{inch}}{2.54\ \text{cm}}\right) \times \left(\frac{1\ \text{foot}}{12\ \text{inches}}\right) = \text{feet}
Calculation:
- Convert 185 cm to inches:
185÷2.54=72.8346 inches185 \div 2.54 = 72.8346\ \text{inches}
- Convert inches to feet:
72.8346÷12=6.0696 feet72.8346 \div 12 = 6.0696\ \text{feet}
Paul’s height is approximately 6.07 feet.
Explanation:
To accurately determine a person’s height in feet when the value is given in centimeters, we must apply a sequential unit conversion. The metric system and the imperial system use different scales, so using correct factors is crucial.
The first step is to convert centimeters to inches. Since 1 inch equals 2.54 centimeters, we divide the original height, 185 cm, by 2.54. This yields roughly 72.83 inches. This intermediary unit gives us a familiar scale in the imperial system and prepares us for the next step.
Then, we convert inches to feet. There are 12 inches in 1 foot, so we divide the result by 12. Dividing 72.83 inches by 12 gives approximately 6.07 feet.
This method demonstrates the use of fraction-based conversion factors to cancel units systematically. Each step ensures the previous unit is replaced cleanly, preserving accuracy. The dimensional analysis used here is widely applicable in science and engineering because it guarantees consistency across measurement systems.
By mastering this process, we reinforce a broader understanding of unit equivalency, and we learn how to map real-world quantities across different systems through logic and arithmetic precision. For interdisciplinary learners like you, this technique connects mathematical computation with practical measurement scenarios.
