Final answer:
To find the number of leading zeros in 1/X, subtract 1 from the absolute value of the negative exponent of X when X is written in scientific notation. The correct method is not explicitly provided as an option in the student's list. The closest incorrect answer given is to subtract the exponent from 1, which is part of the correct process but is not complete or accurate.
Step-by-step explanation:
To find the number of leading zeros when dividing 1/X, where X is a number with a given exponent, we use the concept of negative exponents. A negative exponent signifies that the number is a fraction with a denominator greater than one, thus we are dealing with a decimal number less than one. When looking at scientific notation such as 5 x 10-3, this implies having a decimal point followed by (3-1), which is 2 zeros, and then the digit 5, resulting in 0.005. Therefore, to find the number of leading zeros, you would subtract 1 from the absolute value of the negative exponent. Option B, subtract the exponent of X from 1 is incorrect as this doesn't provide a method to calculate the leading zeros. The correct answer is not listed as an option, but the closest incorrect answer provided by the student is Option B, calling for a subtraction which is involved in the correct process.
Take another example using scientific notation: for 1.6 x 10-2, you would move the decimal two places to the left, yielding 0.016, which has one leading zero. In this case, we subtract 1 from the absolute value of the negative exponent (|-2|-1 = 1), confirming the number of leading zeros.