Problem
Determine 165 pounds in kg. Express the result in kilograms using a correct conversion factor and report an appropriate rounded value for general chemistry measurement work.
Key idea: dimensional analysis (unit cancellation)
Unit conversions in general chemistry are handled by multiplying by a conversion factor written as a ratio so that unwanted units cancel. For pounds to kilograms, use the exact definition \(1\ \text{lb} = 0.45359237\ \text{kg}\).
Step-by-step conversion: 165 lb to kg
Step 1: Write the conversion factor as a ratio.
\[ \frac{0.45359237\ \text{kg}}{1\ \text{lb}} \]
Step 2: Multiply and cancel units.
\[ 165\ \text{lb}\cdot \frac{0.45359237\ \text{kg}}{1\ \text{lb}} = 165\cdot 0.45359237\ \text{kg} = 74.84274105\ \text{kg} \]
Step 3: Round appropriately (significant figures).
The value 165 has 3 significant figures, so a typical chemistry-reporting rounded value is: \[ 74.84274105\ \text{kg} \approx 74.8\ \text{kg} \]
Result summary
| Quantity | Value | Notes (general chemistry reporting) |
|---|---|---|
| Given mass | 165 lb | Imperial unit; often converted to SI for lab calculations |
| Exact conversion factor | \(1\ \text{lb} = 0.45359237\ \text{kg}\) | Definition-based factor |
| Converted mass (unrounded) | \(74.84274105\ \text{kg}\) | Direct multiplication with the factor |
| Converted mass (3 significant figures) | \(74.8\ \text{kg}\) | Matches the significant figures of 165 |
Visualization: mapping 165 lb to kilograms
Common pitfalls
- Inverting the factor: using \(\frac{1\ \text{lb}}{0.45359237\ \text{kg}}\) would produce pounds again, not kilograms.
- Forgetting unit cancellation: keep units explicitly so lb cancels and kg remains.
- Over-rounding too early: carry extra digits during the multiplication, then round at the end to match significant figures.
Final answer
\[ 165\ \text{lb} = 74.84274105\ \text{kg} \approx 74.8\ \text{kg} \]