Solve for the mass of 85.4 kg in units of pounds. 1Ib = 453.6 g
The correct answer and explanation is:
To solve for the mass of 85.4 kg in pounds (lb) using the conversion factor 1 lb = 453.6 g, follow these steps:
Step 1: Convert kilograms to grams
Since 1 kg = 1,000 g: 85.4 kg×1,000=85,400 g85.4 \, \text{kg} \times 1,000 = 85,400 \, \text{g}
Step 2: Convert grams to pounds
Using the conversion factor 1 lb = 453.6 g: 85,400 g÷453.6 g/lb=188.2 lb(rounded to one decimal place)85,400 \, \text{g} \div 453.6 \, \text{g/lb} = 188.2 \, \text{lb} \quad \text{(rounded to one decimal place)}
✅ Final Answer: 188.2 pounds
📘 Explanation (300 words)
Unit conversions are essential in science, engineering, health, and everyday life, allowing us to communicate and apply measurements consistently across systems. The metric system uses kilograms (kg) as a base unit for mass, while the imperial system commonly uses pounds (lb). Converting between these requires a known conversion factor, which in this case is: 1 lb=453.6 g1 \, \text{lb} = 453.6 \, \text{g}
The given mass is 85.4 kg, which we first convert to grams because our conversion factor uses grams. Since 1 kg equals 1,000 grams, multiplying by 1,000 gives us 85,400 grams.
Next, we use dimensional analysis to convert grams to pounds. Dividing the total grams (85,400) by the number of grams in one pound (453.6) provides the result in pounds. This method ensures that units cancel appropriately, leaving us with the desired unit—pounds. 85,400 g453.6 g/lb=188.2 lb\frac{85,400 \, \text{g}}{453.6 \, \text{g/lb}} = 188.2 \, \text{lb}
This calculation is particularly useful in fields such as medicine, where dosages and body weights may be measured in different systems, or in travel and shipping industries, where mass limits might be listed in pounds even if original weights are in kilograms.
Understanding and applying conversions like these ensures accurate communication and measurement, preventing errors that could have significant consequences in professional settings.