Apply powers-of-ten notation: what is the product of 0.0003 and 10^-3 (demonstrate correct handling of negative exponents)?

Introduction / Context:
Scientific notation streamlines tiny and large values commonly seen in electronics (nano, micro, milli). Multiplying by 10^-3 should make a number 1000 times smaller. This item verifies the direction and magnitude of the decimal shift when a negative power is applied.

Given Data / Assumptions:

• Initial number: 0.0003.
• Multiplier: 10^-3 = 0.001.
• Goal: compute 0.0003 × 10^-3 precisely as a decimal.

Concept / Approach:

When multiplying by 10^n, move the decimal point n places: left for negative n, right for positive n. Here n = -3, so move left by three places. Alternatively, multiply by 0.001 directly. Keep significant figures intact during the move to avoid rounding errors in conceptual steps.

Step-by-Step Solution:

Verification / Alternative check:

Convert to scientific notation: 0.0003 = 3 × 10^-4. Multiply by 10^-3 to get 3 × 10^-7, which is 0.0000003. Both methods agree.

Why Other Options Are Wrong:

0.0003 corresponds to multiplying by 10^0, not 10^-3. 3 and 3,000 result from moving the decimal to the right, which would require positive exponents.

Common Pitfalls:

Shifting the decimal in the wrong direction; dropping or adding zeros incorrectly; confusing 10^-3 with division by 3 (it is division by 1000).

Final Answer:

0.0000003