Answer:
104₈
Step-by-step explanation:
In base 10, the expanded form of your number is ...
... 6×10¹ + 8×10⁰
In base 8, the expanded form of your number is ...
... 1×8² + 0×8¹ + 4×8⁰ = 104₈
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<em>How to convert</em>
The usual method of converting an integer to a different number base is taught as ...
- Divide the number by the new base. The remainder is the digit of interest, and the quotient is used for repeating this step. Digits of the converted number are generated right to left.
In this case, the rightmost digit is 68 mod 8 = 4, and the number used for generating the next digit to its left is floor(68/8) = 8.
The next digit is 8 mod 8 = 0, and the number used for generating the next digit to its left is floor(8/8) = 1.
Finally, the most significant digit of the converted number is 1 mod 8 = 1.
The three digits of the base-8 number are then 104.
<em>Alternate Method</em>
This method will develop the digits left to right. It can be used to find the converted value of numbers with fractional parts.
Choose a power of the desired base that is greater than the number to be converted. Here, that might be 8³ = 512. This power tells you the number of digits that will comprise the integer part of the converted number. (Additional digits you may develop will be the fractional part of the converted number.)
Form a fraction with the number as the numerator and with that power as the denominator. (here, 68/512.)
Develop converted digits left to right by ...
- multiply the fraction by the number base. (here, 68/512×8 = 1 4/64.)
- use the integer part of the result as the next digit of the converted number. (here, 1.)
- use the fractional part of the result to repeat these steps from #1. (here, 4/64 will be used.)
