## Thinking Mathematically (6th Edition)

$1580_{nine}$
$(6\times 3)_{10}=(18)_{10}=2\times 9+0=(20)_{9}$ Record the $0$; carry the $2$. $\begin{array}{llll} & 2 & 4 & 3_{nine}\\ \times & & & 6_{nine}\\ -- & -- & -- & --\\ & & & 0_{nine} \end{array}$ $(6\times 4+2)_{10}=(26)_{10}=2\times 9+8=(28)_{9}$ Record the $8$; carry the $2$. $\begin{array}{llll} & 2 & 4 & 3_{nine}\\ \times & & & 6_{nine}\\ -- & -- & -- & --\\ & & 8 & 0_{nine} \end{array}$ $(6\times 2+2)_{10}=(14)_{10}=1\times 9+5=(15)_{9}$ Record the $15.$ Result: $1580_{nine}$