Convert 145 pounds to kilograms using dimensional analysis and unit fractions.
The Correct Answer and Explanation is :
To convert 145 pounds to kilograms using dimensional analysis and unit fractions, we start by knowing the conversion factors between pounds and kilograms. Specifically, 1 pound is approximately equal to 0.453592 kilograms. We can use this information to set up our conversion.
Step-by-Step Conversion:
- Identify the Conversion Factor:
We know that:
[
1 \text{ lb} = 0.453592 \text{ kg}
] - Set Up the Dimensional Analysis:
We can express 145 pounds in terms of kilograms by multiplying by the conversion factor. Using unit fractions helps us ensure that the units will cancel out correctly, leading us to the desired unit of kilograms. The conversion setup looks like this:
[
145 \text{ lb} \times \frac{0.453592 \text{ kg}}{1 \text{ lb}}
] - Perform the Calculation:
Now we perform the multiplication:
[
145 \times 0.453592 = 65.77064 \text{ kg}
] - Final Result:
Thus,
[
145 \text{ lb} \approx 65.77 \text{ kg}
]
Explanation of Dimensional Analysis:
Dimensional analysis is a method used to convert units from one measurement system to another. It relies on the idea of using conversion factors that relate different units. In this case, we used a conversion factor (0.453592 kg/lb) that allows us to transition from pounds to kilograms.
By organizing our calculations into a format where units can cancel out, we ensure that the resulting value maintains the correct dimensions. The unit fraction, which is a ratio of equivalent measurements, serves to facilitate this cancellation. For example, when we multiply by (\frac{0.453592 \text{ kg}}{1 \text{ lb}}), the “pound” units cancel out, leaving us with the unit we desire (kilograms).
This method is particularly useful in scientific and engineering calculations, where accurate unit conversions are essential. It ensures clarity and prevents mistakes that can arise from miscalculating unit conversions, making it a valuable technique in various fields. In conclusion, using dimensional analysis not only provides the correct numerical result but also reinforces a systematic approach to unit conversion.