Compare the products: (0.1667)(0.8333)(0.3333) versus (0.2222)(0.6667)(0.1250). Which is larger?

Problem restatementDecide which of the two given decimal products has the greater value.

Given data

• A = 0.1667 × 0.8333 × 0.3333
• B = 0.2222 × 0.6667 × 0.1250

Concept/ApproachEstimate each term to familiar fractions (0.1667 ≈ 1/6, 0.8333 ≈ 5/6, 0.3333 ≈ 1/3, 0.2222 ≈ 2/9, 0.6667 ≈ 2/3, 0.1250 = 1/8), or compute directly with careful decimals.

Step-by-Step calculation A ≈ 0.1667 × 0.8333 = 0.1389 (approx), then × 0.3333 ≈ 0.0463 B ≈ 0.2222 × 0.6667 = 0.1481 (approx), then × 0.1250 ≈ 0.0185 Therefore, A ≈ 0.0463 and B ≈ 0.0185 ⇒ A > B

Verification/AlternativeFractional check: (1/6)(5/6)(1/3) = 5/108 ≈ 0.046296, while (2/9)(2/3)(1/8) = 4/216 = 1/54 ≈ 0.018519. Left is clearly larger.

Common pitfalls

• Assuming equality because both look like products of small decimals.
• Rounding too coarsely; here the order of magnitude differs by about 2.5×.

Final AnswerLeft product is larger