Compute and express in scientific notation: (27.5 × 10^3) + (8.9 × 10^4) = ?

Introduction / Context:
Combining numbers in scientific notation is routine in circuit calculations, such as summing charge, energy, or resistance values reported at different scales. Correctly aligning powers of ten and normalizing the result keeps the final answer concise and comparable.

Given Data / Assumptions:

• Two quantities: 27.5 × 10^3 and 8.9 × 10^4.
• We must add them and express the sum in normalized scientific notation (one nonzero digit before the decimal point).
• Standard arithmetic rules for powers of ten apply.

Concept / Approach:
For addition, convert both terms to the same exponent, then add mantissas. After summing, renormalize the coefficient if needed so it lies between 1 and 10, adjusting the exponent accordingly.

Step-by-Step Solution:

Verification / Alternative check:
Convert to plain numbers: 27,500 + 89,000 = 116,500. Back to scientific notation: 116,500 = 1.165 × 10^5. Matches the computed result.

Why Other Options Are Wrong:

• 36.4 × 10^7: Exponent and mantissa are both incorrect; far too large.
• 116.5 × 10^4: Not normalized; correct value but coefficient must be between 1 and 10.
• 28.39 × 10^3: Arithmetic error from adding mantissas without aligning exponents correctly.

Common Pitfalls:
Adding mantissas with different exponents directly or failing to renormalize; always align exponents first, then adjust the final exponent so the coefficient is within [1, 10).

Final Answer:
1.165 × 10^5