Question

The number 1982 in the decimal system when written in the base 12 is:

• A. 1182
• B. 1912
• C. 1192
• D. 1292

Hint:

When converting to another base, use successive division and read remainders in reverse order.

Answer 1

The Correct Option is C

Step 1: Divide by 12 repeatedly \[ 1982 \div 12 = 165 \text{ remainder } 2 \] \[ 165 \div 12 = 13 \text{ remainder } 9 \] \[ 13 \div 12 = 1 \text{ remainder } 1 \] \[ 1 \div 12 = 0 \text{ remainder } 1 \] Step 2: Read remainders from last to first $1 \ 1 \ 9 \ 2$ (base 12) Thus: \[ 1982_{10} = 1192_{12} \] \[ \boxed{1192} \]