Difficulty: Easy
Correct Answer: Incorrect
Explanation:
Introduction / Context:Scientific notation standardizes how we write large and small numbers: a × 10^n with 1 ≤ a < 10. This convention improves readability, prevents zeros from being dropped or added accidentally, and facilitates clear comparison of magnitudes in datasheets and calculations.
Given Data / Assumptions:
Concept / Approach:In scientific notation, the mantissa a must be at least 1 and less than 10. The exponent n is an integer. Writing 560,000 does not show a power of ten or a normalized mantissa. The correct scientific notation is 5.6 × 10^5 (or 5.600 × 10^5 if more significant digits are justified by measurement).
Step-by-Step Solution:
Express 560,000 with one nonzero digit to the left of the decimal: 5.6.Count decimal shifts: five places to the left from 560,000 to 5.6 → 10^5.Combine: 5.6 × 10^5.Conclude: 560,000 as typed is not scientific notation.Verification / Alternative check:Engineering notation groups powers by 3: 560,000 = 560 × 10^3. This is engineering notation (mantissa between 1 and 999), not scientific notation. Both are valid formats, but the rules differ; the prompt asked about scientific notation specifically.
Why Other Options Are Wrong:
Correct: ignores the requirement to show the power of ten and normalized mantissa.Unit-based or rounding-based claims do not change the definition of scientific notation.“Engineering but not scientific” is close conceptually, but the original 560,000 is not written as 560 × 10^3 either.Common Pitfalls:Assuming any compact form qualifies; omitting the exponent; confusing engineering notation (steps of 10^3) with scientific notation (1 to 10 mantissa).
Final Answer:Incorrect
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