Questions: Write 287 in the base-twelve system. 287=□twelve

Solution Steps

To convert the number 287 from base ten to base twelve, we repeatedly divide the number by 12 and record the remainders. The remainders, read in reverse order, give the digits of the number in base twelve.

To convert \( 287 \) from base ten to base twelve, we perform repeated division by \( 12 \) and keep track of the remainders.

1. \( 287 \div 12 = 23 \) with a remainder of \( 11 \).
2. \( 23 \div 12 = 1 \) with a remainder of \( 11 \).
3. \( 1 \div 12 = 0 \) with a remainder of \( 1 \).

The remainders collected from the divisions are \( 1, 11, 11 \). Reading these from last to first gives us the base twelve representation. In base twelve, \( 11 \) is represented as \( B \).

Thus, \( 287 \) in base twelve is \( 1BB_{12} \).

Final Answer