Unit conversion in electrical power: How many kilowatts (kW) are contained in 135 milliwatts (mW)? Convert the given power using SI prefixes and express the final answer in kW, not in watts.

Introduction / Context:
Engineering calculations require fluent conversion between SI units. Here we convert a small power value given in milliwatts (mW) into kilowatts (kW), reinforcing how metric prefixes relate through powers of ten.

Given Data / Assumptions:

• Given power: 135 mW.
• 1 W is the base SI unit of power.
• milli (m) = 10^-3; kilo (k) = 10^3.
• Goal: express the result in kilowatts (kW).

Concept / Approach:
First convert milliwatts to watts, then convert watts to kilowatts. Using powers of ten keeps the process systematic and error-free. You can also jump directly from mW to kW by combining prefixes: 1 mW = 10^-6 kW because 10^-3 W and 1 kW = 10^3 W.

Step-by-Step Solution:

Verification / Alternative check:
Direct conversion using prefix algebra: 135 mW = 135 * 10^-6 kW = 1.35 * 10^-4 kW. Both routes match exactly.

Why Other Options Are Wrong:

• 135 × 10–3 kW: Equals 0.135 kW, which is 135 W, three orders too large.
• 0.0135 kW: Equals 13.5 W, still two orders too large.
• 0.00135 kW: Equals 1.35 W, one thousand times too large.

Common Pitfalls:

• Mistaking mW → kW as 10^-3 rather than 10^-6 relative to kW.
• Dropping or misplacing the decimal when shifting powers of ten.

Final Answer:
1.35 × 10–4 kW