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BECE Mathematics 2011 Paper

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Question : 7

Total: 40

Convert

222_{\text{five }}

to a number in base ten.

30
52
60
62

Solution:

Concept:

Convert a base-five numeral to base ten by expanding it in powers of

5

.

Explanation:

Write

222_{\text{five}}

using powers of

5

.

222_{\text{five}} = 2 \times 5^2 + 2 \times 5^1 + 2 \times 5^0

Compute each term:

2 \times 5^2 = 2 \times 25 = 50

2 \times 5^1 = 2 \times 5 = 10

2 \times 5^0 = 2 \times 1 = 2

Now add the results:

50 + 10 + 2 = 62

Answer:

222_{\text{five}} = 62_{_{ten}}

The correct option is D. 62.

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