Final answer:
In base seven, the least four-digit number is 1000 (7) and its decimal equivalent is 1000 (10). The greatest four-digit number in base seven is 6665 (7) and its decimal equivalent is 3762 (10).
Step-by-step explanation:
In base seven, the least four-digit number is seven, which is equal to ten in decimal. The decimal equivalent of the least four-digit number is 1000.
The greatest four-digit number in base seven is 6665. To find the decimal equivalent, we need to convert each digit to decimal. Using the place value system, we have ((6 * 7^3) + (6 * 7^2) + (6 * 7^1) + (5 * 7^0)) = 3421 + 294 + 42 + 5 = 3762.
Therefore, the least four-digit number in base seven and its decimal equivalent is 1000 (7) and 1000 (10), respectively. The greatest four-digit number in base seven and its decimal equivalent is 6665 (7) and 3762 (10), respectively. The correct choice is option D.