When 95.75 is multiplied by 0.2554, how many digits will appear to the right of the decimal point in the final product?

Introduction:
This question examines your understanding of how decimal places behave during multiplication of decimal numbers. Instead of requiring full multiplication, the problem focuses only on counting the total number of digits to the right of the decimal point in the resulting product.

Given Data / Assumptions:

• First number: 95.75.
• Second number: 0.2554.
• We must find the number of digits to the right of the decimal point in the product 95.75 * 0.2554.
• No rounding or truncation is applied; we consider the exact product.

Concept / Approach:
When two decimal numbers are multiplied, the total number of decimal places in the product equals the sum of the decimal places in each factor. We do not need to actually multiply the numbers to answer this question; we simply count decimal digits in each number and add them.

Step-by-Step Solution:
Step 1: Count decimal digits in 95.75. It has 2 digits after the decimal point (7 and 5). Step 2: Count decimal digits in 0.2554. It has 4 digits after the decimal point (2, 5, 5, and 4). Step 3: Total decimal digits in the product = 2 + 4 = 6. Step 4: Therefore, the product 95.75 * 0.2554 will have 6 digits to the right of the decimal point.

Verification / Alternative check:
If you remove the decimals temporarily, you can think of 95.75 as 9575 / 100 and 0.2554 as 2554 / 10000. Their product is (9575 * 2554) / (100 * 10000) = some integer divided by 10^6, which clearly has 6 decimal places. This confirms the result without needing the exact product value.

Why Other Options Are Wrong:

• 7, 8, or 9: These would require more decimal digits than the sum of the original decimal places, which is not possible with straightforward multiplication.
• 5: This would require one fewer decimal place than the sum, which does not match the rule that decimal places add in multiplication.

Common Pitfalls:
Learners sometimes miscount decimal places, especially when there is a leading zero before the decimal. Remember that only digits after the decimal point are counted, and the total number in the product is the sum from both factors. There is no need to perform the full multiplication for such questions.

Final Answer:
The product will have 6 digits to the right of the decimal point.