Answer
↓Steps Explained:↓
Convert 227 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 >= 227
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 227
Since 512 is greater than 227, 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 227 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 <= 227, 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 227 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 <= 227, 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 227 is 3
Multiplying this coefficient by our original value, we get: 3 * 1 = 3
Add our new value to our running total, we get:
224 + 3 = 227
This = 227, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 227
Our octal notation is now equal to 343
Final Answer
We are done. 227 converted from decimal to octal notation equals 3438.Take the Quiz
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