Answer
↓Steps Explained:↓
Convert 115 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 >= 115
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 115
Since 512 is greater than 115, 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 115 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 <= 115, 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 115 is 6
Multiplying this coefficient by our original value, we get: 6 * 8 = 48
Add our new value to our running total, we get:
64 + 48 = 112
This is <= 115, so we assign our outside coefficient of 6 for this digit.
Our new sum becomes 112
Our octal notation is now equal to 16
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 115 is 3
Multiplying this coefficient by our original value, we get: 3 * 1 = 3
Add our new value to our running total, we get:
112 + 3 = 115
This = 115, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 115
Our octal notation is now equal to 163
Final Answer
We are done. 115 converted from decimal to octal notation equals 1638.Take the Quiz
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