Difficulty: Easy
Correct Answer: Correct
Explanation:
Introduction / Context:Scientific notation is essential in electronics because measured quantities often span many orders of magnitude. Representing numbers as a mantissa multiplied by a power of ten reduces confusion, keeps units consistent, and minimizes transcription errors when dealing with very small or very large values such as microvolts, megaohms, and nanofarads.
Given Data / Assumptions:
Concept / Approach:To write a number in scientific notation, move the decimal point so that exactly one nonzero digit remains to its left. Count the places moved; left-to-right movement for small values yields a negative exponent. The numeric value must remain identical after scaling by the proper power of ten, and the unit stays unchanged unless an explicit unit conversion is performed.
Step-by-Step Solution:
Start with 0.00015 V.Move the decimal 4 places to the right to get 1.5.Compensate with 10^–4 because moving right increases the number; the negative exponent brings it back: 1.5 × 10^–4.Attach the original unit: 1.5 × 10^–4 V.Verification / Alternative check:Compute 1.5 × 10^–4 = 1.5 / 10,000 = 0.00015, confirming exact equality. If desired, convert to microvolts: 0.00015 V = 150 µV (since 1 V = 10^6 µV). Both representations are consistent.
Why Other Options Are Wrong:
Incorrect: contradicts the correct power-of-ten placement.0.15 × 10^–3 V equals 1.5 × 10^–4 V numerically, but the mantissa is not between 1 and 10, so it is not standard scientific notation.“Only for millivolts” and “cannot be expressed” are false; scientific notation is universal across units.Common Pitfalls:Mixing up sign of the exponent; changing the unit without adjusting the exponent; writing a mantissa outside 1 to 10 range and calling it “scientific notation.”
Final Answer:Correct
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