Nested division with decimals: Evaluate 0.15 ÷ (0.5 ÷ 15) by simplifying the inner division first and then completing the outer operation.

Introduction / Context:Nested divisions can be simplified by working from the inside out. This problem also reinforces that dividing by a fraction is equivalent to multiplying by its reciprocal, a crucial concept in decimal and fraction arithmetic alike.

Given Data / Assumptions:

• Expression: 0.15 ÷ (0.5 ÷ 15)
• All numbers are exact decimals.

Concept / Approach:First evaluate the inner operation 0.5 ÷ 15. Then divide 0.15 by that result. Alternatively, note that 0.5 ÷ 15 = 1/30, so the overall expression becomes 0.15 ÷ (1/30) = 0.15 × 30.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 45: Treats 0.15 as 15, ignoring decimals.
• 0.03 or 0.45: Arise from inverting the wrong term or dropping a factor of 10.

Common Pitfalls:

• Performing outer division first, against order of operations.
• Misinterpreting 0.5 ÷ 15 as 0.5 × 15.

Final Answer: