Convert a whole number to scientific notation: express 65,000 as a value between 1 and 10 multiplied by an appropriate power of ten.

Introduction / Context:
Scientific notation represents numbers as a coefficient between 1 and 10 multiplied by a power of ten. This standard form is crucial for clear communication in engineering and science, especially when comparing magnitudes across many orders of magnitude.

Given Data / Assumptions:

• Number to convert: 65,000.
• Target format: a × 10^n with 1 ≤ a < 10.

Concept / Approach:

Move the decimal point so that exactly one non-zero digit remains to its left. The number of places moved to the left determines the positive exponent on 10. Verify by expanding back to the original decimal form.

Step-by-Step Solution:

Verification / Alternative check:

Expand: 6.5 × 10^4 = 6.5 × 10,000 = 65,000. The representation matches exactly and satisfies the 1–10 coefficient requirement.

Why Other Options Are Wrong:

0.65 × 10^4 = 6,500 (too small). 65 × 10^4 = 650,000 (too large). 650 × 10^3 = 650,000 (also too large and coefficient not in 1–10).

Common Pitfalls:

Leaving the coefficient outside 1–10; miscounting how many places the decimal is moved; mixing up 10^3 and 10^4.

Final Answer:

6.5 × 10^4