Scientific vs. engineering notation: Identify the key differences between these two ways of expressing numbers.

Introduction / Context:
Both scientific and engineering notation help manage very large and very small numbers, but they follow different formatting rules. Engineers prefer engineering notation for easy alignment with SI prefixes (kilo, milli, micro), while scientists often use scientific notation for normalized representation and significant-figure clarity.

Given Data / Assumptions:

• Scientific notation requires exactly one nonzero digit before the decimal point.
• Engineering notation constrains exponents to multiples of 3.
• Both use powers of ten but with different normalization conventions.

Concept / Approach:
Scientific notation: a × 10^n with 1 ≤ a < 10. Engineering notation: b × 10^(3k) with 1 ≤ b < 1000 (one to three digits before the decimal), which aligns directly with SI prefixes (10^3 ↔ kilo, 10^6 ↔ mega, 10^−3 ↔ milli, etc.).

Step-by-Step Solution:

Verification / Alternative check:
Convert 47,000: scientific = 4.7 × 10^4; engineering = 47 × 10^3 (47 k). The latter maps cleanly to k-units, confirming practical advantage in engineering contexts.

Why Other Options Are Wrong:

• Each single statement captures a partial difference; the best complete description is that all listed differences apply.

Common Pitfalls:
Reporting engineering notation with more than three digits before the decimal or forgetting to adjust the exponent by multiples of three when shifting the decimal point.

Final Answer:
All of the above