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WAEC Mathematics 2022 Paper

Question : 2

Total: 47

Change 432

_{five}

to a number in base three.

Solution:

Concept:

Convert the given base-5 number to base 10 first, then convert that decimal value to base 3 by repeated division.

Explanation:

Write

432_{5}

using powers of 5.

432_{5} = (4 \times 5^{2}) + (3 \times 5^{1}) + (2 \times 5^{0})

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

= 100 + 15 + 2 = 117_{10}

Now divide

117

by 3 repeatedly and record each remainder.

117 \div 3 = 39

remainder

0

39 \div 3 = 13

remainder

0

13 \div 3 = 4

remainder

1

4 \div 3 = 1

remainder

1

1 \div 3 = 0

remainder

1

Read the remainders from bottom to top.

117_{10} = 11100_{3}

Therefore,

432_{5} = 11100_{3}

Answer:

11100_{3}

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