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BECE Mathematics 2013 Paper

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Question : 6

Total: 40

Convert

2114_{\;\text{five }\;}

to a base ten numeral.

194
280
284
300

Solution:

Concept:

To convert a base five numeral to base ten, multiply each digit by the corresponding power of

5

and add the results.

Explanation:

Write

2114_{\text{five}}

in expanded form using powers of

5

.

The rightmost digit has power

5^0

, then

5^1

,

5^2

, and

5^3

moving left.

So,

2114_{\text{five}} = 2 \times 5^3 + 1 \times 5^2 + 1 \times 5^1 + 4 \times 5^0

.

Evaluate each term:

2 \times 5^3 = 2 \times 125 = 250

1 \times 5^2 = 1 \times 25 = 25

1 \times 5^1 = 1 \times 5 = 5

4 \times 5^0 = 4 \times 1 = 4

Add all the values:

250 + 25 + 5 + 4 = 284

Thus,

2114_{\text{five}}

equals

284

in base ten.

Answer:

Option C:

284

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