Test Index

BECE Mathematics 2014 Paper

Question : 7

Total: 40

Convert

243_{\text{five}}

Solution:

Concept:

To convert a numeral from another base to base ten, multiply each digit by the power of the base according to its place value, then add the results.

Explanation:

Write

243_{\text{five}}

using powers of

5

The digit

2

is in the

5^2

place,

4

is in the

5^1

place, and

3

is in the

5^0

place.

So,

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

Since

5^0 = 1

, this becomes

(2 \times 25) + (4 \times 5) + (3 \times 1)

Now calculate:

50 + 20 + 3 = 73

Answer:

243_{\text{five}} = 73

, so the correct option is D. 73.

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