Final answer:
The greatest 6-digit number with the given digits is 876,420, and the least is 204,678 (not starting with zero). The difference between these two numbers is 671,742. Marcus is incorrect in his notation of the least number, as it should not start with zero or contain a decimal point.
Step-by-step explanation:
The student is working with the concept of arranging digits to form the greatest and least 6-digit numbers and calculating the difference between them. When arranging digits to form the greatest possible number, we start with the largest digit and place them in descending order. Conversely, for the least possible number, we start with the smallest non-zero digit, since a number cannot start with zero.
a. The greatest 6-digit number is 876,420.
b. The least 6-digit number is 204,678 (not 024,678, because the number cannot start with zero).
c. To find the difference, subtract the smaller number from the larger number: 876,420 - 204,678 = 671,742.
d. Marcus is incorrect in writing 024.678 for the least 6-digit number. A number cannot start with a zero and should not contain a decimal point if it is meant to be an integer.