When 85.44 is multiplied by 0.08455, how many digits will there be to the right of the decimal point in the product?

Introduction / Context:
This problem checks your understanding of how decimal places behave when two decimal numbers are multiplied. Instead of calculating the full product of 85.44 and 0.08455, we only need to determine how many digits will appear to the right of the decimal point in the final result. This is a standard concept in working with decimals and helps in quick estimation.

Given Data / Assumptions:

• First decimal number: 85.44.
• Second decimal number: 0.08455.
• We need the total number of digits to the right of the decimal point in their product.
• No rounding is mentioned; we count all decimal digits resulting from exact multiplication.

Concept / Approach:
When multiplying two decimals, the total number of digits to the right of the decimal point in the product is equal to the sum of the numbers of digits to the right of the decimal points in each factor. This rule comes from the fact that moving the decimal point is equivalent to multiplying or dividing by powers of 10. We use this rule without computing the actual product value, which saves time and avoids arithmetic mistakes.

Step-by-Step Solution:
Step 1: Count the number of digits to the right of the decimal point in 85.44.Step 2: In 85.44, there are 2 digits after the decimal point (4 and 4).Step 3: Count the number of digits to the right of the decimal point in 0.08455.Step 4: In 0.08455, there are 5 digits after the decimal point (0, 8, 4, 5, and 5).Step 5: Add these counts: 2 + 5 = 7.Step 6: Therefore the product 85.44 × 0.08455 will have 7 digits to the right of the decimal point.

Verification / Alternative check:
To verify, imagine removing the decimal points and treating the numbers as integers, then adjusting the decimal afterwards. 85.44 can be seen as 8544 / 100, and 0.08455 can be seen as 8455 / 100000. Their product is (8544 * 8455) / (100 * 100000) = (8544 * 8455) / 10^7. Since the denominator is 10^7, the decimal representation of the product will have 7 digits after the decimal point, which matches our earlier count.

Why Other Options Are Wrong:
Option 5: Ignores the decimal places of one of the factors or miscounts them.Option 4: May come from counting only digits after the decimal in one number.Option 6: Represents adding incorrectly, for example 2 + 5 and then subtracting 1 by mistake.Option 8: Overestimates the total number of decimal places; there is no basis for this count from the given numbers.

Common Pitfalls:
A common mistake is to miscount the digits after the decimal point, especially when there are leading zeros, as in 0.08455. Students sometimes count 4 digits instead of 5. Another error is to think that multiplication somehow shortens the decimal part, which is not true in general. Always remember: the number of decimal places in the product is the sum of the decimal places in the factors.

Final Answer:
The product has 7 digits to the right of the decimal point.