Change \(432_{five}\) to a number in base three.

Convert from base 5 to base 10

432five ${}_{\mathrm{<br>}}$ =  (4 x 52 ${}^2$) + (3 x 51 ${}^1$) + (2 x 50 ${}^0$)

= (4 x 25) + (3 x 5) + (2 x 1)

= 100 + 15 + 2

= 117ten ${}_{\mathrm{<br>}}$

Then convert from base 10 to base 3

Selecting the remainders from bottom to top:

117ten ${}_{\mathrm{<br>}}$ = 11100three ${}_{\mathrm{<br>}}$

Hence; 432five ${}_{\mathrm{<br>}}$ =  11100three