Compute the decimal product accurately: 8.32 × 0.999. Use the idea that 0.999 = 1 − 0.001 for a quick evaluation.

Introduction / Context:Multiplying by 0.999 can be done very quickly by using the identity 0.999 = 1 − 0.001. This method reduces multiplication to a simple subtraction, minimizing rounding errors and mental effort.

Given Data / Assumptions:

• Value to compute: 8.32 × 0.999
• All decimals are exact; do not round prematurely.

Concept / Approach:Rewrite 0.999 as 1 − 0.001. Then 8.32 × 0.999 = 8.32 × (1 − 0.001) = 8.32 − 0.00832. Simple subtraction then yields the precise product.

Step-by-Step Solution:0.999 = 1 − 0.001.8.32 × 0.999 = 8.32 − (8.32 × 0.001) = 8.32 − 0.00832.Result = 8.31168.

Verification / Alternative check:Standard multiplication also gives 8.31168. You can cross-check by noting that the answer must be slightly less than 8.32 (by exactly 0.00832).

Why Other Options Are Wrong:

• 8.31668 or 8.31618: Subtracting 0.00332 or 0.00382 instead of 0.00832.
• 0.831168: Misplaced decimal point by one order of magnitude.
• 8.32168: Incorrectly adding instead of subtracting the small adjustment.

Common Pitfalls:Misplacing the decimal when computing 8.32 × 0.001; adding rather than subtracting; copying errors in digits.

Final Answer:8.31168