Power units and metric prefixes Confirm whether the electrical power value 4,200 W is numerically equal to 4.2 kW when expressed using the kilo (10^3) prefix.

Introduction / Context:Working across datasheets and test reports, engineers routinely convert raw watt values using SI prefixes to keep numbers readable and comparable. Misapplying prefixes can lead to 10× or 1000× errors with costly consequences, especially in power budgeting and thermal design.

Given Data / Assumptions:

• Base unit for power: watt (W).
• kilo (k) denotes multiplication by 10^3.
• No change in the physical quantity, only unit scaling.

Concept / Approach:To convert W to kW, divide by 10^3. The relationship is P(kW) = P(W) / 1000. Conversely, multiply kW by 1000 to return to W. This conversion is independent of AC or DC context, power factor, or frequency; it is purely a unit scaling within the SI system.

Step-by-Step Solution:

Verification / Alternative check:Express in megawatts: 4,200 W = 0.0042 MW because 1 MW = 10^6 W. Each form is consistent as long as the power-of-ten factor is applied correctly.

Why Other Options Are Wrong:

Common Pitfalls:Confusing k (10^3) with K (kelvin); writing “KW” instead of “kW”; mixing k (10^3) with Ki (kibi, 2^10) which is not used for SI power units.

Final Answer:Correct