Engineering notation identification: Which of the following numbers is correctly written in engineering notation (mantissa between 1 and 1000, exponent a multiple of 3)?

Introduction / Context:
Engineering notation is a variant of scientific notation where the exponent of ten is a multiple of 3. This aligns neatly with metric prefixes (k, M, G, m, μ, n, p), aiding readability in circuit values and specifications. Recognizing correct engineering notation improves communication and reduces conversion errors.

Given Data / Assumptions:

• Proper engineering notation requires: 1 ≤ mantissa < 1000 and exponent ∈ {..., −9, −6, −3, 0, 3, 6, 9, ...}.
• We evaluate each option against these criteria.

Concept / Approach:

Check the exponent first for a multiple of 3, then ensure the mantissa is within the [1, 1000) interval. If either fails, the representation is not engineering notation (even though it can be a valid numeric expression).

Step-by-Step Solution:

Verification / Alternative check:

Convert to SI prefixes: 9.1 × 10^−6 = 9.1 μ (micro-units), which is exactly the convenience engineering notation provides—easy mapping to metric prefixes.

Why Other Options Are Wrong:

• Non-multiple-of-3 exponents break the engineering-notation requirement.
• Mantissas outside [1, 1000) are not in standard engineering format.

Common Pitfalls:

• Confusing scientific and engineering notation; the latter locks exponents to multiples of 3.
• Leaving mantissas like 0.91 instead of renormalizing to 910 × 10^−9 if desired.

Final Answer:

9.1 × 10^−6