Arrange the following in ascending order of magnitude \(110_{two}, 31_{eight}, 42_{five}\)
A
\(110_{two}, 31_{five}, 42_{eight}\)
B
\(42_{five}, 110_{two}, 31_{eight}\)
C
\(42_{five}, 31_{eight}, 110_{two}\)
D
\(110_{two}, 42_{five}, 31_{eight}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Converting each number to base 10
\(110_{two} = 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0\)
= 1 \times 4 + 1 \times 2 + 0 \times 1
= 4 + 2 + 0
= \(6_{ten}\)
\(31_{eight} = 3 \times 8^1 + 1 \times 8^0\)
= 3 \times 8 + 1 \times 1
= 24 + 1
= \(25_{ten}\)
\(42_{five} = 4 \times 5^1 + 2 \times 5^0\)
= 4 \times 5 + 2 \times 1
= 20 + 2
= \(22_{ten}\)
Hence, \(31_{eight} > 42_{five} > 110_{two}\)
In ascending order, \(110_{two}, 42_{five}, 31_{eight}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #69124)