Arrange the following in ascending order of magnitude 110_{{two}}, 31_{{eight}}, 42_{{five}}

Correct Answer is : 110two,42five,31eight110_{{two}}, 42_{{five}}, 31_{{eight}}110two,42five,31eight

110_{{two}}, 31_{{five}}, 42_{{eight}}

42_{{five}}, 110_{{two}}, 31_{{eight}}

42_{{five}}, 31_{{eight}}, 110_{{two}}

110_{{two}}, 42_{{five}}, 31_{{eight}}

Correct Answer is : 110two,42five,31eight110_{{two}}, 42_{{five}}, 31_{{eight}}110two,42five,31eight

Test Index

WAEC Mathematics 2023 Paper

Question : 24

Total: 50

110_{\text{two}}, 31_{\text{eight}}, 42_{\text{five}}

Solution:

Concept:

Compare numbers written in different bases by converting each to base

10

Explanation:

Convert

110_{\text{two}}

to base

10

110_{\text{two}} = 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0

= 4 + 2 + 0 = 6

Convert

31_{\text{eight}}

to base

10

31_{\text{eight}} = 3 \times 8^1 + 1 \times 8^0

= 24 + 1 = 25

Convert

42_{\text{five}}

to base

10

42_{\text{five}} = 4 \times 5^1 + 2 \times 5^0

= 20 + 2 = 22

Now compare the base

10

values:

6 < 22 < 25

So,

110_{\text{two}} < 42_{\text{five}} < 31_{\text{eight}}

Answer:

Ascending order:

110_{\text{two}}, 42_{\text{five}}, 31_{\text{eight}}

Correct option: D

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