Answer
$1230_{\text{four}}$
Work Step by Step
The place values of base four are: $..., 4^4, 4^3, 4^2, 4^1, 1$.
The place values that are less than or equal to $108$ are $4^3$, $4^2$, $4^1$, and $1$
Divide $108$ by $4^3$ or $64$ to obtain:
$108 \div 64 = 1$ remainder $44$
Divide the remainder $44$ by $4^2$ or $16$ to obtain:
$44 \div 16 = 2$ remainder $12$
Divide the remainder $12$ by $4^1$ or $4$ to obtain:
$12 \div 4 = 3$ remainder $0$
Divide the remainder $0$ by $1$ to obtain:
$0 \div 1 = 0$ remainder $0$
Thus,
$108=(1 \times 4^3) + (2 \times 4^2) + (3 \times 4^1) + (0 \times 1)
\\108=1230_{\text{four}}$
