Scientific notation check — evaluate the statement: “Subtracting 18 × 10^2 from 480 × 10^1 gives 30 × 10^2.” Is this arithmetic statement valid?

Introduction / Context:Scientific notation is a compact way to handle large and small numbers in electronics, physics, and engineering calculations. This problem asks you to validate a subtraction expressed in scientific-notation style and to recognize appropriate normalization.

Given Data / Assumptions:

• Two quantities: 480 × 10^1 and 18 × 10^2.
• We are checking the raw arithmetic equivalence, not significant figures or unit conversions.
• No units are attached; treat both numbers as pure magnitudes.

Concept / Approach:The easiest way to verify is to convert both terms into ordinary integers and perform the subtraction, then re-express the result in scientific notation. Alternatively, align powers of ten and subtract the mantissas accordingly.

Step-by-Step Solution:

Verification / Alternative check:Normalize further to strict scientific notation if desired: 3000 = 3.0 × 10^3. Both 30 × 10^2 and 3.0 × 10^3 represent the same value; the latter is preferred when the mantissa is between 1 and 10.

Why Other Options Are Wrong:

• Incorrect: The arithmetic does check out; the equality holds.
• Valid only if units cancel / Cannot be determined: Units are not involved here; it is purely numeric.

Common Pitfalls:Forgetting to align exponents or misplacing the decimal when renormalizing. Always convert to ordinary numbers or match exponents before subtracting.

Final Answer:Correct — 480 × 10^1 − 18 × 10^2 equals 30 × 10^2.