The value of (3.6 × 0.48 × 2.50) ÷ (0.12 × 0.09 × 0.5) is:

To evaluate a product/quotient of decimal numbers, convert every decimal into a whole number by multiplying it by the appropriate power of 10; as long as the SAME overall power of 10 is applied to both the numerator and the denominator, the value of the expression is unchanged. The resulting whole-number fraction can then be simplified by cancelling common factors term by term.

1. Clear the decimals in the numerator: 3.6 × 10 = 36, 0.48 × 100 = 48, and 2.50 × 100 = 250 — an overall numerator scaling factor of 10 × 100 × 100 = 100000.

2. Clear the decimals in the denominator the same way: 0.12 × 100 = 12, 0.09 × 100 = 9, and 0.5 × 10 = 5 — an overall denominator scaling factor of 100 × 100 × 10 = 100000.

3. Since the numerator and the denominator were both scaled by the same factor (100000), the value of the expression is unchanged: (3.6 × 0.48 × 2.50) ÷ (0.12 × 0.09 × 0.5) = (36 × 48 × 250) ÷ (12 × 9 × 5).

4. Cancel common factors term by term: 36 ÷ 9 = 4, 48 ÷ 12 = 4, and 250 ÷ 5 = 50.

5. Multiply the reduced terms: 4 × 4 × 50 = 800.

Cross-check: Multiplying out fully gives 36 × 48 × 250 = 432000 in the numerator and 12 × 9 × 5 = 540 in the denominator, and 432000 ÷ 540 = 800 — confirming the cancelled result.

So the value of the expression is 800.