Express 4.38 × 10^-3 using an equivalent coefficient multiplied by 10^-6 (convert between powers of ten accurately).

Introduction / Context:
Changing the exponent base (e.g., from 10^-3 to 10^-6) without altering the value is a common maneuver when aligning like units or combining measurements in electronics and physics. The goal is to keep the numerical value identical while expressing it with a different power of ten.

Given Data / Assumptions:

• Original form: 4.38 × 10^-3.
• Target form: something × 10^-6.
• Algebraic identity: 10^-3 = 10^3 × 10^-6.

Concept / Approach:

To replace 10^-3 with 10^-6, multiply the coefficient by 10^3 so the overall magnitude remains unchanged. This trades exponent for coefficient: a smaller exponent needs a larger coefficient by the same power of ten, and vice versa.

Step-by-Step Solution:

Verification / Alternative check:

Convert to decimal: 4.38 × 10^-3 = 0.00438. Also, 4,380 × 10^-6 = 4,380 × 0.000001 = 0.00438. Both equal, so the transformation is correct.

Why Other Options Are Wrong:

438 × 10^-6 = 0.000438 (too small by factor 10). 43,800 × 10^-6 = 0.0438 (too large). 438,000 × 10^-6 = 0.438 (much too large).

Common Pitfalls:

Forgetting to balance the exponent change by the coefficient; miscounting zeros when multiplying by 10^3.

Final Answer:

4,380 × 10^-6