Resistance unit conversion: how many megohms (MΩ) are contained in 0.03 kilohms (kΩ)?

Introduction / Context:
Resistance values appear with many prefixes. Precise conversion among Ω, kΩ, and MΩ prevents major mistakes in design and troubleshooting. This exercise turns a small kilohm value into megohms, illustrating multi-step prefix changes.

Given Data / Assumptions:

• Given: 0.03 kΩ.
• 1 kΩ = 10^3 Ω, 1 MΩ = 10^6 Ω.
• Goal: express the result in MΩ.

Concept / Approach:

First convert kilohms to ohms, then convert ohms to megohms. Because mega is three orders of magnitude larger than kilo, going from kΩ to MΩ divides by 1000 directly. Alternatively, convert all the way to ohms and then back up to megohms using powers of ten to avoid confusion.

Step-by-Step Solution:

Verification / Alternative check:

Direct k→M step: 0.03 kΩ ÷ 1000 = 0.00003 MΩ = 3 × 10^-5 MΩ. Both methods agree.

Why Other Options Are Wrong:

0.00002 MΩ and 0.0002 MΩ are off by factors of 2/3 or 10. The choice “either … or …” is incorrect because there is only one exact value.

Common Pitfalls:

Confusing k with M; moving the decimal the wrong way; skipping units during conversion leading to misplaced zeros.

Final Answer:

3 × 10^-5 MΩ