Answer
↓Steps Explained:↓
Convert 270 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 >= 270
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 270
Since 512 is greater than 270, 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 270 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 <= 270, 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 270 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
256 + 8 = 264
This is <= 270, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 264
Our octal notation is now equal to 41
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 270 is 6
Multiplying this coefficient by our original value, we get: 6 * 1 = 6
Add our new value to our running total, we get:
264 + 6 = 270
This = 270, so we assign our outside coefficient of 6 for this digit.
Our new sum becomes 270
Our octal notation is now equal to 416
Final Answer
We are done. 270 converted from decimal to octal notation equals 4168.Take the Quiz Switch to Chat Mode
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