Evaluate a nested decimal expression accurately: 3 / [ 3 + {(0.3 − 3.03) / (3 × 0.91)} ] = ?

Introduction / Context:This question checks precision with signed decimals and order of operations inside a complex denominator. Spotting simple cancellation makes the computation almost trivial once the inner fraction is recognized.

Given Data / Assumptions:

• Expression: 3 / [ 3 + {(0.3 − 3.03) / (3 × 0.91)} ]
• All decimal arithmetic is exact; keep the sign when subtracting.

Concept / Approach:Simplify the inner fraction first by computing its numerator and denominator. If they share magnitude (up to sign), the fraction becomes −1. Then evaluate the outer denominator and finally perform the division.

Step-by-Step Solution:Inner numerator: 0.3 − 3.03 = −2.73.Inner denominator: 3 × 0.91 = 2.73.Thus inner fraction = −2.73 / 2.73 = −1.Overall denominator: 3 + (−1) = 2.Final value: 3 / 2 = 1.5.

Verification / Alternative check:Convert to fractions out of 100 (e.g., 0.91 = 91/100) and observe exact cancellation to confirm the −1 step rigorously.

Why Other Options Are Wrong:

• 15: As if multiplying instead of dividing by 2.
• 0.75: Inverts the final fraction 3/2 improperly.
• 1.75 and 1.25: Arise from arithmetic slips in the denominator (e.g., adding signs incorrectly).

Common Pitfalls:Losing the negative sign from 0.3 − 3.03; miscomputing 3 × 0.91 as 2.79; or forgetting to simplify the inner term before the outer operations.

Final Answer:1.5