Scientific notation and powers of ten: Express the number 4,500,000 in proper scientific form.

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:

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