The value of (3.157 × 4126 × 3.198) ÷ (63.972 × 2835.121) is closest to:

Concept

To quickly estimate the value of a product or quotient of several decimal numbers, round each number to a nearby convenient value that keeps a similar order of magnitude, then simplify the resulting fraction by cancellation before doing any division.

Applying it here

1. Round each factor to a nearby convenient value: 3.157 → 3.2, 3.198 → 3.2, 63.972 → 64 (keep 4126 and 2835.121 → 2835 at the same scale).

2. Substitute the rounded values into the expression: (3.2 × 4126 × 3.2) ÷ (64 × 2835).

3. Write each 3.2 as 32⁄10, so the two extra factors of 10 pull out as ÷100: (32 × 4126 × 32) ÷ (64 × 2835) × 1⁄100.

4. Cancel 32 × 32 ÷ 64 = 16, leaving (16 × 4126) ÷ 2835 × 1⁄100 = 66016 ÷ 2835 × 1⁄100.

5. Divide: 66016 ÷ 2835 ≈ 23.28, so the expression ≈ 23.28 ÷ 100 = 0.2328 ≈ 0.23.

Cross-check

As a quick order-of-magnitude check, rougher rounding (3 × 4126 × 3) ÷ (64 × 2835) ≈ 37134 ÷ 181440 ≈ 0.205, confirming the value lands close to 0.2 and not any of the other choices, which differ by a factor of 10 or more.

So the expression is closest to 0.2.