Change 432\(_{five}\) to a number in base three.
A
10100\(_{three}\)
B
11100\(_{three}\)
C
11101\(_{three}\)
D
10110\(_{three}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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\(_{three}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64425)