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JAMB Mathematics 2018 Paper

Question : 48

Total: 62

Calculate 243

_{six}

_{five}

expressing your answer in base 10

Solution:

Concept:

Convert each number in a different base into base 10, then subtract the resulting values.

Explanation:

Convert

243_{\text{six}}

to base 10:

243_{\text{six}} = (2 \times 6^2) + (4 \times 6^1) + (3 \times 6^0)

= 72 + 24 + 3 = 99

in base 10.

Convert

243_{\text{five}}

to base 10:

243_{\text{five}} = (2 \times 5^2) + (4 \times 5^1) + (3 \times 5^0)

= 50 + 20 + 3 = 73

in base 10.

Now subtract the two base-10 values:

99 - 73 = 26

Answer:

26

in base 10, i.e. option C.

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