Answer
$123_{\text{five}}$
Work Step by Step
To convert a numeral in base eight to a numeral in base five, the following steps must be performed:
(1) Convert the numeral in base eight to base ten.
$46_{\text{eight}}=(4\times 8^1) + (6 \times 1)=32+6=38$
(2) Convert the result in Step (1) to a numeral in base five using division.
The place values in base five are: $5^2, 5^1, 1$.
The place values less than or equal to 38 are: $5^2, 5^1,$ and $1$.
Divide $38$ by $5^2$ or $25$:
$38 \div 25 = 1$ remainder $13$
Divide $13$ by $5^1$ or $5$:
$13 \div 5 = 2$ remainder $3$
Divide $3$ by $1$:
$3 \div 1 =3$
Thus,
$38 = (1 \times 5^2) + (2 \times 5^1) + (3 \times 1)
\\38= 123_{\text{five}}$
