Units and magnitudes in circuit analysis: What is the correct equivalent value of 1 megaohm (1 MΩ) expressed in ohms?

Introduction / Context:Accurate unit conversions are essential in electronics. Confusing kilo (10^3), mega (10^6), and milli (10^−3) leads to major design and measurement errors. This item checks your comfort with SI prefixes as applied to resistance units (ohms).

Given Data / Assumptions:

• Prefix definitions: k = 10^3, M = 10^6, m = 10^−3, μ = 10^−6.
• Target: convert 1 MΩ to Ω.
• Context: typical datasheets use these prefixes regularly.

Concept / Approach:Apply SI prefix conversion: 1 megaohm = 1 × 10^6 ohms. Compare with common confusions: 1 kΩ = 10^3 Ω; one-millionth of an ohm is micro-ohm (μΩ), not megaohm.

Step-by-Step Solution:Identify prefix: M = 10^6.Compute: 1 MΩ = 1 × 10^6 Ω.State in words: one million ohms.

Verification / Alternative check:Cross-check with other prefixes: 1 kΩ = 1,000 Ω confirms that mega is three orders of magnitude larger than kilo.

Why Other Options Are Wrong:(a) 1 kΩ is 1,000 Ω, not 1 MΩ. (b) 100,000 Ω equals 100 kΩ. (c) One-millionth of an ohm is 1 μΩ, the inverse of mega in exponent sign.

Common Pitfalls:Mixing up M (mega) with m (milli) due to case sensitivity; always respect uppercase vs lowercase in SI.

Final Answer:1,000,000 Ω (one million ohms)