How many digits will be there to the right of the decimal point in the product of 95.75 and .02554?

Concept & Logic The total number of decimal places in a product is initially the sum of the decimal places in the factors. However, if the multiplication of the trailing integers results in zeros, those trailing zeros cancel out the corresponding decimal places. Step-by-Step Solution * Count the initial decimal places: $95.75$ has 2, and $0.02554$ has 5. * The maximum number of decimal places in the product is $2 + 5 = 7$. * Now, look at the integer multiplication: $9575 \times 2554$. * Focus on the last digits to see if a trailing zero is formed: $5 \times 4 = 20$. This creates exactly one trailing zero. * Let's verify if there is a second zero by multiplying the last two digits of each number: $75 \times 54 = 4050$. The product ends in `50`, meaning there is only one trailing zero at the very end. * That single trailing zero drops off the end of the decimal. * Effective decimal places = Total initial places - Number of trailing zeros = $7 - 1 = 6$. Exam Strategy & Shortcut You never need to calculate the full product. Just add the decimal counts ($2 + 5 = 7$) and multiply the last two digits of the numbers ($75 \times 54 = 4050$) to check for trailing zeros. Finding one zero immediately drops the significant decimal count from 7 to 6. Common Pitfall The most common mistake is simply adding the decimal places ($2 + 5 = 7$) and immediately choosing option (c), completely ignoring how trailing zeros functionally eliminate decimal places in final standardized numbers. Final Answer **Therefore, the correct answer is 6.**