In power units, 1 kilowatt (1 kW) is equal to how many watts (W)?

Introduction / Context:
Electrical and mechanical power are often expressed in watts and kilowatts. Understanding the relationship between these units is essential when reading power ratings of household appliances, motors, and power plants. This question asks you to convert one kilowatt into its equivalent number of watts.

Given Data / Assumptions:

• The base SI unit of power is the watt (W).
• The prefix kilo means one thousand times the base unit.
• We want to know how many watts are contained in 1 kilowatt.
• We assume standard SI prefixes and definitions.

Concept / Approach:
The SI system uses prefixes to denote multiples and submultiples of base units. The prefix kilo, with symbol k, denotes a factor of 10^3, which equals 1000. This rule applies uniformly across units: one kilometre is 1000 metres, one kilogram is 1000 grams in older usage, and one kilowatt is 1000 watts. Therefore, converting from kilowatts to watts simply means multiplying the numerical value by 1000.

Step-by-Step Solution:
Step 1: Recall the SI prefix rule: 1 kilo unit = 1000 base units. Step 2: Apply this rule to power: 1 kilowatt = 1 kilo watt. Step 3: Replace kilo with 1000: 1 kilowatt = 1000 watts. Step 4: Express this result in compact form: 1 kW = 1000 W. Step 5: Select the option that matches this numeric equivalence, which is 1000 W.

Verification / Alternative check:
Consider a household appliance rated at 0.5 kW. Converting to watts gives 0.5 * 1000 = 500 W. This matches typical power values for devices like microwave ovens or small heaters. Power plants are often rated in megawatts, where 1 MW = 1000 kW = 1,000,000 W, again showing the consistent factor of 1000 between kilowatt and watt. These examples reinforce the simple conversion factor.

Why Other Options Are Wrong:
10 W: This would imply that kilo represents a factor of 10, which conflicts with the SI definition of kilo. 100 W: This would treat kilo as 100, again inconsistent with the standard prefix. 10000 W: This corresponds to a factor of 10^4 and would be appropriate for 10 kW, not 1 kW.

Common Pitfalls:
Some learners mix up kilo and mega or forget that SI prefixes are powers of ten. Confusion can also arise from using non SI units such as horsepower alongside watts. To avoid mistakes, remember that 1 kW = 1000 W and that 1 MW = 1000 kW. Writing out the factors in powers of ten, such as 10^3 and 10^6, can help maintain clarity when converting between units.

Final Answer:
One kilowatt is equal to 1000 W (1000 watts).