How many digits will appear to the right of the decimal point in the product of 95.75 and 0.2554, based on decimal place counting rules?

Introduction / Context:
This question is about understanding how many decimal places appear in the product of two decimal numbers. It targets a very common rule taught in schools: the total number of digits to the right of the decimal point in a product equals the sum of the digits to the right of the decimal point in the factors, ignoring later simplification or cancellation.

Given Data / Assumptions:

• We are multiplying 95.75 by 0.2554.
• 95.75 has two digits after the decimal point.
• 0.2554 has four digits after the decimal point.
• We are asked how many digits will be to the right of the decimal point in the product by using the standard counting rule.

Concept / Approach:
The usual method for estimating the number of decimal digits in a product is to ignore the decimal points, multiply the numbers as integers, and then count the total number of decimal places by adding the decimal digits from each factor. That sum tells us how many digits to place to the right of the decimal in the final result before any simplification is considered.

Step-by-Step Solution:
First count the decimal places in 95.75. It has two digits after the decimal: 7 and 5.Next count the decimal places in 0.2554. It has four digits after the decimal: 2, 5, 5, and 4.Add these together: 2 + 4 = 6.Therefore, when 95.75 and 0.2554 are multiplied, the product will have six digits to the right of the decimal point according to the standard rule.So the answer is 6.

Verification / Alternative check:
If you actually perform the multiplication or use a calculator, you will find that the product is 24.45455. In this specific case, the full product may simplify and appear with fewer effective decimal digits. However, the method taught in aptitude and basic arithmetic typically asks you to apply the counting rule based on the original decimal places before simplification, which gives six decimal places as the expected result. The question is clearly focused on this rule rather than on simplification details.

Why Other Options Are Wrong:
Options 7, 8, and 9 assume more decimal digits than the sum of the original decimal places, which contradicts the rule. Option 5 assumes fewer digits and arises from noticing that the actual decimal representation may simplify, but that is not what the standard classroom rule asks you to count. The teaching focus is on adding the decimal places from both factors, leading to exactly six digits to the right of the decimal point.

Common Pitfalls:
Some learners mistakenly count the digits to the left of the decimal or mix them up with digits to the right. Others believe that the number of decimal places might change unpredictably with multiplication, which is not true when you consider the raw product before simplification. Always count the digits to the right of the decimal in each factor and add them to get the total decimal places in the product.

Final Answer:
Based on the standard decimal counting rule, the product of 95.75 and 0.2554 will have 6 digits to the right of the decimal point.