Answer
↓Steps Explained:↓
Convert 285 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 >= 285
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 285
Since 512 is greater than 285, 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 285 is 4
Multiplying this coefficient by our original value, we get: 4 * 64 = 256
Add our new value to our running total, we get:
0 + 256 = 256
This is <= 285, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 256
Our octal notation is now equal to 4
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 285 is 3
Multiplying this coefficient by our original value, we get: 3 * 8 = 24
Add our new value to our running total, we get:
256 + 24 = 280
This is <= 285, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 280
Our octal notation is now equal to 43
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 285 is 5
Multiplying this coefficient by our original value, we get: 5 * 1 = 5
Add our new value to our running total, we get:
280 + 5 = 285
This = 285, so we assign our outside coefficient of 5 for this digit.
Our new sum becomes 285
Our octal notation is now equal to 435
Final Answer
We are done. 285 converted from decimal to octal notation equals 4358.Take the Quiz
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