Choose the correct answer from the decimal to octal conversion given below.
(0.125)10 = (0.100)8
To convert a decimal number to its octal equivalent, especially fractional parts, follow these steps:
- Multiply the decimal fraction by 8 (since we are converting to octal, base 8).
- Record the integer part of the result as the next octal digit.
- Subtract the integer part from the result and multiply the new fractional part by 8 again.
- Continue this process until the fractional part becomes zero or you have achieved the desired precision.
Let's convert the given decimal fraction \((0.125)_{10}\) to its octal equivalent:
- First multiplication: \(0.125 \times 8 = 1.000\)
The integer part is 1, and the fractional part is 0. Hence, the octal representation stops here because the fractional part has become zero.
Therefore, \((0.125)_{10}\) is equivalent to \((0.1)_{8}\) in octal.
This matches the correct answer: (0.125)10 = (0.100)8
Other options can be dismissed because:
- (0.200)8, (0.300)8, and (0.400)8 do not correctly represent the fractional conversion steps shown above.
Thus, the correct conversion of \((0.125)_{10}\) to octal is indeed \((0.100)_{8}\).
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