WAEC 2023 · Paper 1 · Q19

Arrange the following in ascending order of magnitude: $110_{\text{two}}$ , $31_{\text{eight}}$ , $42_{\text{five}}$ .

Worked solution (try it first)

Change each to base ten: $110_{\text{two}} = 4 + 2 = 6$ , $31_{\text{eight}} = 24 + 1 = 25$ and $42_{\text{five}} = 20 + 2 = 22$ .
In ascending order: $6 < 22 < 25$ .
So the order is $110_{\text{two}}, 42_{\text{five}}, 31_{\text{eight}}$ , option B.