Scientific notation alignment — express with 10^1: The number 5200 × 10^–2 is equal to what value multiplied by 10^1?

Introduction / Context:Proficiency with scientific notation prevents mistakes when scaling numbers or matching units. In electronics, powers of ten appear everywhere: impedance at different frequencies, RC time constants, or converting between prefixes like kilo and milli. This item practices re-expressing a quantity with a different power of ten while keeping the value identical.

Given Data / Assumptions:

• Original expression: 5200 × 10^–2.
• Target form: X × 10^1 (find X).
• Basic rule: shifting the exponent by +3 requires shifting the coefficient by ÷1000, etc.

Concept / Approach:First simplify the original form to a plain number, then rebuild it using the required base of 10^1. Alternatively, keep the value constant by adjusting the coefficient and exponent inversely: if the exponent increases by +3, the coefficient must be divided by 10^3, and vice versa.

Step-by-Step Solution:

Verification / Alternative check:Adjust exponents: 5200 = 5.2 × 10^3. Then 5200 × 10^–2 = 5.2 × 10^(3–2) = 5.2 × 10^1. This directly yields X = 5.2.

Why Other Options Are Wrong:52 would demand 52 × 10^1 = 520, not 52. 0.52 × 10^1 = 5.2, not 52. 520 × 10^1 = 5200, and 0.052 × 10^1 = 0.52; both incorrect.

Common Pitfalls:Forgetting that changing the exponent requires compensating the coefficient so the overall value is unchanged, and mixing up decimal shifts in the wrong direction.

Final Answer:5.2