Compute the product 12.5 × 3.2 × 8.8 by converting decimals if needed and select the correct result.

Introduction / Context:
This question checks fluency with multiplication of decimal numbers. Products like 12.5 × 3.2 × 8.8 often appear in quantitative tests to see whether candidates can handle place values and decimals confidently. A common strategy is to convert decimals into fractions with denominators that are powers of 10 and then multiply and simplify.

Given Data / Assumptions:

• Expression: 12.5 × 3.2 × 8.8.

• All numbers are terminating decimals, so they can be expressed as simple fractions.

• We seek an exact integer result that matches one of the options.

Concept / Approach:
We write each decimal as a fraction: 12.5 as 125/10, 3.2 as 32/10 and 8.8 as 88/10. Then we multiply these fractions, combine numerators and denominators, and simplify step by step. Another method is to group factors cleverly to make round numbers like 10 or 100, reducing the chance of errors. Both methods should lead to the same final integer value.

Step-by-Step Solution:
Step 1: Convert decimals to fractions: 12.5 = 125/10, 3.2 = 32/10 and 8.8 = 88/10. Step 2: Multiply: 12.5 × 3.2 × 8.8 = (125/10) × (32/10) × (88/10). Step 3: Combine numerators and denominators: (125 × 32 × 88) / (10 × 10 × 10) = (125 × 32 × 88) / 1000. Step 4: Multiply stepwise. First 125 × 32 = 4000. Step 5: Next multiply 4000 × 88 = 352000. Step 6: Now divide by 1000: 352000 / 1000 = 352.

Verification / Alternative check:
We can estimate the magnitude by approximating each factor. 12.5 is about 12, 3.2 is about 3, and 8.8 is about 9. The rough product 12 × 3 × 9 = 324, which is in the same ballpark as 352. A more careful mental grouping is also possible: 12.5 × 8.8 = (25/2) × (88/10) = (25 × 88) / 20. Since 25 × 88 = 2200, we have 2200 / 20 = 110. Then 110 × 3.2 = 110 × (32/10) = (110 × 32) / 10 = 3520 / 10 = 352. Both methods confirm the same result.

Why Other Options Are Wrong:
Values like 358, 355, 354 and 356 are close to 352 but do not match the exact product. These options represent typical rounding or small arithmetic errors. Since the arithmetic above is exact and uses integer operations after converting decimals to fractions, there is no ambiguity. Thus only 352 correctly represents the product 12.5 × 3.2 × 8.8.

Common Pitfalls:
Common errors include misplacing the decimal point after multiplication, for example counting the total number of decimal places incorrectly. Another mistake is partially rounding one factor before multiplying, which may shift the result away from the exact value. Converting to fractions or strategically grouping factors to form tens and hundreds reduces reliance on decimal place counting and improves accuracy.

Final Answer:
The exact value of 12.5 × 3.2 × 8.8 is 352.