Answer
↓Steps Explained:↓
Convert 231 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 >= 231
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 231
Since 512 is greater than 231, 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 231 is 3
Multiplying this coefficient by our original value, we get: 3 * 64 = 192
Add our new value to our running total, we get:
0 + 192 = 192
This is <= 231, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 192
Our octal notation is now equal to 3
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 231 is 4
Multiplying this coefficient by our original value, we get: 4 * 8 = 32
Add our new value to our running total, we get:
192 + 32 = 224
This is <= 231, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 224
Our octal notation is now equal to 34
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 231 is 7
Multiplying this coefficient by our original value, we get: 7 * 1 = 7
Add our new value to our running total, we get:
224 + 7 = 231
This = 231, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 231
Our octal notation is now equal to 347
Final Answer
We are done. 231 converted from decimal to octal notation equals 3478.Take the Quiz
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