To convert 999 to base seven, we perform repeated division by 7 and collect the remainders, which yields the digits 2, 6, 2 and 5 in base 7. Reading them from most significant to least significant gives 2625₇. Expanding 2625₇ as 2×7³ + 6×7² + 2×7¹ + 5 gives 686 + 294 + 14 + 5 = 999. Hence 2625 is the correct base-seven representation of 999.
Option A:
2624₇ expands as 2×343 + 6×49 + 2×7 + 4 = 686 + 294 + 14 + 4 = 998. Because it is one less than 999, it cannot be the correct base-seven form. This is a typical near-miss distractor in conversion questions.
Option B:
2665₇ equals 2×343 + 6×49 + 6×7 + 5 = 686 + 294 + 42 + 5 = 1027. This value is larger than 999, so it does not match the required decimal. The higher middle digits inflate the base-seven value.
Option C:
2635₇ represents 2×343 + 6×49 + 3×7 + 5 = 686 + 294 + 21 + 5 = 1006. Since 1006 is slightly above 999, this cannot be the correct representation. It again illustrates sensitivity to changes in the lower-order digits.
Option D:
2625₇ when expanded gives 686 + 294 + 14 + 5 = 999. That matches the decimal value exactly, confirming its correctness. This option reflects accurate execution of repeated division and positional weighting in base-seven conversions.
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