Answer
↓Steps Explained:↓
Convert 280 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 >= 280
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 280
Since 512 is greater than 280, 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 280 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 <= 280, 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 280 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 = 280, 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 280 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
280 + 1 = 281
This is > 280, so we assign a 0 for this digit.
Our total sum remains the same at 280
Our octal notation is now equal to 430
Final Answer
We are done. 280 converted from decimal to octal notation equals 4308.Take the Quiz Switch to Chat Mode
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