Answer
↓Steps Explained:↓
Convert 298 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 >= 298
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 298
Since 512 is greater than 298, 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 298 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 <= 298, 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 298 is 5
Multiplying this coefficient by our original value, we get: 5 * 8 = 40
Add our new value to our running total, we get:
256 + 40 = 296
This is <= 298, so we assign our outside coefficient of 5 for this digit.
Our new sum becomes 296
Our octal notation is now equal to 45
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 298 is 2
Multiplying this coefficient by our original value, we get: 2 * 1 = 2
Add our new value to our running total, we get:
296 + 2 = 298
This = 298, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 298
Our octal notation is now equal to 452
Final Answer
We are done. 298 converted from decimal to octal notation equals 4528.Take the Quiz
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