Approximate (nearest sensible option): 6885.009 − 419.999 − 94.989 = ?

Introduction:
When subtracting near-integers, round each term to the nearest whole and compute. The residual decimals are small and typically cancel or adjust by less than 1–2 units, which the coarse options easily accommodate.

Given Data / Assumptions:

• Start: 6885.009
• Subtract: 419.999 and 94.989

Concept / Approach:
Approximate each: 6885, 420, and 95. Compute 6885 − 420 − 95 quickly and select the closest listed option. This is the standard technique for fast mental arithmetic with slight decimal tails.

Step-by-Step Solution:

Verification / Alternative check:
Exact arithmetic: 6885.009 − 419.999 − 94.989 = 6370. (The decimals nearly cancel to an integer.)

Why Other Options Are Wrong:
6650 and 6830 are too large; 6200 is too small; 6400 overshoots slightly. 6370 matches both the approximate and exact computations.

Common Pitfalls:
Subtracting in the wrong order or mis-rounding 419.999 down to 419; nearest rounding gives a cleaner computation path.

Final Answer:
6370