Scientific notation and powers of ten: Express the number 4,500,000 in proper scientific form.
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A4,500 × 10^6
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B4.5 × 10^6
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C4.5 × 10^-3
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Deither 4,500 × 10^4 or 4.5 × 10^6
Answer
Correct Answer: 4.5 × 10^6
Explanation
Introduction / Context:Scientific notation represents numbers as a coefficient between 1 (inclusive) and 10 (exclusive) multiplied by a power of ten. It is essential for communicating large and small values succinctly in engineering, physics, and computing.
Given Data / Assumptions:
- Target number: 4,500,000.
- Scientific notation format: a × 10^n, where 1 ≤ a < 10 and n is an integer.
Concept / Approach:Move the decimal point so that only one non-zero digit remains to the left of the decimal; count how many places you moved and set that as the exponent n (positive for large numbers).
Step-by-Step Solution:
Write 4,500,000 with an explicit decimal: 4,500,000.0.Move the decimal 6 places to the left to get 4.5 → coefficient a = 4.5.Because we moved left by 6 places, multiply by 10^6 → final form 4.5 × 10^6.Verification / Alternative check:Reverse the operation: 4.5 × 10^6 = 4.5 × 1,000,000 = 4,500,000. Options like 4,500 × 10^4 evaluate to 45,000,000, which is not equal to 4,500,000.
Why Other Options Are Wrong:
- 4,500 × 10^6: Coefficient is not between 1 and 10; also equals 4.5 × 10^9, far too large.
- 4.5 × 10^-3: Represents 0.0045, not a large number.
- either 4,500 × 10^4 or 4.5 × 10^6: The first expression equals 45,000,000, which is incorrect.
Common Pitfalls:
- Forgetting the coefficient range rule (1 ≤ a < 10).
- Miscounting decimal shifts, leading to an exponent error by powers of ten.
Final Answer:4.5 × 10^6