Evaluate powers of ten: The quantity 3.3 × 10^3 equals which of the following standard decimal forms?

Introduction / Context:Scientific notation expresses numbers compactly as a coefficient times a power of ten. Converting back and forth prevents place-value mistakes when entering data into calculators or spreadsheets.

Given Data / Assumptions:

• Given: 3.3 × 10^3.
• 10^3 means shift the decimal three places to the right.
• Goal: choose the correct decimal representation.

Concept / Approach:Multiply the coefficient 3.3 by 1000. Moving the decimal right expands the value by three orders of magnitude, preserving significant digits (here, two significant figures: 3.3).

Step-by-Step Solution:

Verification / Alternative check:Place-value shift: 3.3 → 33.0 (10^1) → 330.0 (10^2) → 3300.0 (10^3). The result is 3,300 exactly.

Why Other Options Are Wrong:

• 330: Corresponds to 3.3 × 10^2, not 10^3.
• 33,000: Would be 3.3 × 10^4.
• 0.0033: Would be 3.3 × 10^-3.

Common Pitfalls:

• Shifting the decimal the wrong direction for positive exponents.
• Dropping significant digits when expanding notation.

Final Answer:3,300