Answer
↓Steps Explained:↓
Convert 108 from decimal to octal
(base 8) notation:
Power Test
Raise our base of 8 to a power
Start at 0 and increasing by 1 until it is >= 108
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 108
Since 512 is greater than 108, we use 1 power less as our starting point which equals 2
Build octal notation
Work backwards from a power of 2
We start with a total sum of 0:
82 = 64
The highest coefficient less than 7 we can multiply this by to stay under 108 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
0 + 64 = 64
This is <= 108, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 64
Our octal notation is now equal to 1
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 108 is 5
Multiplying this coefficient by our original value, we get: 5 * 8 = 40
Add our new value to our running total, we get:
64 + 40 = 104
This is <= 108, so we assign our outside coefficient of 5 for this digit.
Our new sum becomes 104
Our octal notation is now equal to 15
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 108 is 4
Multiplying this coefficient by our original value, we get: 4 * 1 = 4
Add our new value to our running total, we get:
104 + 4 = 108
This = 108, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 108
Our octal notation is now equal to 154
Final Answer
We are done. 108 converted from decimal to octal notation equals 1548.Take the Quiz
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