Answer
$3013_{\text{four}}$
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 $199$ are $4^3$, $4^2$, $4^1$, and $1$
Divide $199$ by $4^3$ or $64$ to obtain:
$199 \div 64 = 3$ remainder $7$
Divide the remainder $7$ by $4^2$ or $16$ to obtain:
$7 \div 16 = 0$ remainder $7$
Divide the remainder $7$ by $4^1$ or $4$ to obtain:
$7 \div 4 = 1$ remainder $3$
Divide the remainder $3$ by $1$ to obtain:
$3 \div 1 = 3$ remainder $0$
Thus,
$199=(3 \times 4^3) + (0 \times 4^2) + (1 \times 4^1) + (3 \times 1)
\\199=3013_{\text{four}}$