What is the decimal equivalent of the octal number 325.412?

[amp_mcq option1=”5195.213″ option2=”339.5195″ option3=”5195.339″ option4=”213.5195″ correct=”option4″]

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UPSC CBI DSP LDCE – 2023

To convert an octal number (base 8) to a decimal number (base 10), we multiply each digit by the corresponding power of 8 and sum the results.
For the integer part (325):
3 * 8^2 + 2 * 8^1 + 5 * 8^0
= 3 * 64 + 2 * 8 + 5 * 1
= 192 + 16 + 5
= 213

For the fractional part (.412):
4 * 8^-1 + 1 * 8^-2 + 2 * 8^-3
= 4/8 + 1/64 + 2/512
= 0.5 + 0.015625 + 0.00390625
= 0.51953125

Combining the parts: 213.51953125…
Looking at the options, 213.5195 is the closest representation of the decimal equivalent.

Octal to decimal conversion involves summing the products of each digit and the base (8) raised to the power of its position (positive for integer part, negative for fractional part).

The position of a digit to the left of the radix point starts at 0 and increases by 1 for each position further left. The position of a digit to the right of the radix point starts at -1 and decreases by 1 for each position further right.

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