#### Answer

$473 = 122112_{\text{three}}$

#### Work Step by Step

The place values for base three are $...,3^5, 3^4, 3^3, 3^2, 3^1, 1$.
The place values that are less than or equal to $473$ are $3^5, 3^4, 3^3, 3^2, 3^1, 1$.
Divide $473$ by $3^5$ or $243$:
$473 \div 243 = 1$ remainder $230$
Divide the remainder $230$ by $3^4$ or $81$:
$230 \div 81 = 2$ remainder $68$
Divide the remainder $28$ by $3^3$ or $27$:
$68 \div 27 = 2$ remainder $14$
Divide the remainder $14$ by $3^2$ or $9$:
$14 \div 9 = 1$ remainder $5$
Divide the remainder $5$ by $3^1$ or $3$:
$5 \div 3 = 1$ remainder $2$
Divide the remainder $2$ by $1$:
$2 \div 1 = 2$
Thus,
$473 = (1 \times 3^5) + (2 \times 3^4) + (2 \times 3^3) + (1 \times 3^2) +(1 \times 3^1)+ (2 \times 1)
\\473 = 122112_{\text{three}}$