Quick division estimate near round numbers: Evaluate 750.0003 ÷ 19.999 and select the nearest option.

Introduction / Context:
This division is very close to 750 ÷ 20, a classic mental-math benchmark. Small deviations (750.0003 instead of 750, and 19.999 instead of 20) create only tiny changes to the exact quotient, so the nearest choice is apparent after a quick check.

Given Data / Assumptions:

• N ≈ 750
• D ≈ 20
• We need the nearest option to N/D.

Concept / Approach:
Compute the basic benchmark: 750 ÷ 20 = 37.5. Since the actual denominator is slightly smaller (19.999), the true quotient will be slightly larger than 37.5. Hence, the best nearby whole-number choice is 38.

Step-by-Step Solution:

Verification / Alternative check:
Compute more tightly: 750.0003 ÷ 19.999 ≈ 37.502, which rounds to 38. Back-multiplication: 38 * 19.999 ≈ 759.962, reasonably near 750 with rounding tolerance for a nearest-choice question.

Why Other Options Are Wrong:

• 49, 22, 18, 35: not near the 37.5–38 reference range.

Common Pitfalls:
Rounding in the wrong direction (assuming a larger denominator) or forgetting that a smaller denominator increases the quotient slightly above the 37.5 baseline.

Final Answer:
38