Answer
↓Steps Explained:↓
Convert 184 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 >= 184
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 184
Since 512 is greater than 184, 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 184 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 <= 184, 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 184 is 7
Multiplying this coefficient by our original value, we get: 7 * 8 = 56
Add our new value to our running total, we get:
128 + 56 = 184
This = 184, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 184
Our octal notation is now equal to 27
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 184 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
184 + 1 = 185
This is > 184, so we assign a 0 for this digit.
Our total sum remains the same at 184
Our octal notation is now equal to 270
Final Answer
We are done. 184 converted from decimal to octal notation equals 2708.Take the Quiz
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