Convert the base 5 number 234_5 to a base 10 (decimal) number. What is the value in base 1… — JAMB UTME

Convert the base 5 number $234_5$ to a base 10 (decimal) number. What is the value in base 10?

Answer: 69

The decimal (base 10) equivalent of

234_5

is 69.

Expanding

234_5

gives

(2 \times 5^2) + (3 \times 5^1) + (4 \times 5^0) = 50 + 15 + 4 = 69

Write out the positional expansion of

234_5

using powers of 5 starting from position 0 on the right.

234_5 = (2 \times 5^2) + (3 \times 5^1) + (4 \times 5^0)

Converting from any non-decimal base to base 10 involves multiplying each digit by its corresponding positional base power.

Evaluate the powers of 5 and multiply by the respective digits.

2 \times 25 = 50

3 \times 5 = 15

4 \times 1 = 4

Apply basic arithmetic exponents:

5^2=25

5^1=5

5^0=1

Sum all calculated values together.

50 + 15 + 4 = 69

Adding the positional values yields the total value in base 10.

Converting a non-decimal number to base 10 using expansion by powers of the base.

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