Answer
↓Steps Explained:↓
Convert 165 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 >= 165
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 165
Since 512 is greater than 165, 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 165 is 2
Multiplying this coefficient by our original value, we get: 2 * 64 = 128
Add our new value to our running total, we get:
0 + 128 = 128
This is <= 165, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 128
Our octal notation is now equal to 2
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 165 is 4
Multiplying this coefficient by our original value, we get: 4 * 8 = 32
Add our new value to our running total, we get:
128 + 32 = 160
This is <= 165, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 160
Our octal notation is now equal to 24
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 165 is 5
Multiplying this coefficient by our original value, we get: 5 * 1 = 5
Add our new value to our running total, we get:
160 + 5 = 165
This = 165, so we assign our outside coefficient of 5 for this digit.
Our new sum becomes 165
Our octal notation is now equal to 245
Final Answer
We are done. 165 converted from decimal to octal notation equals 2458.Take the Quiz Switch to Chat Mode
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