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

  • A 10100\(_{three}\)
  • B 11100\(_{three}\)
  • C 11101\(_{three}\)
  • D 10110\(_{three}\)
waec 2022mathematics

The correct answer is B. 11100\(_{three}\)

Convert from base 5 to base 10 432\(_{five}\) =  (4 x 5\(^2\)) + (3 x 5\(^1\)) + (2 x 5\(^0\)) = (4 x 25) + (3 x 5) + (2 x 1) = 100 + 15 + 2 = 117\(_{ten}\) Then convert from base 10 to base 3
3 117
3 39 r 0
3 13 r 0
3 4 r 1
3 1 r 1
  0 r 1
Selecting the remainders from bottom to top: 117\(_{ten}\) = 11100\(_{three}\) Hence; 432\(_{five}\) =  11100\(_{three}\) Previous question Next question