Answer
↓Steps Explained:↓
Convert 210 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 >= 210
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 210
Since 512 is greater than 210, 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 210 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 <= 210, 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 210 is 2
Multiplying this coefficient by our original value, we get: 2 * 8 = 16
Add our new value to our running total, we get:
192 + 16 = 208
This is <= 210, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 208
Our octal notation is now equal to 32
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 210 is 2
Multiplying this coefficient by our original value, we get: 2 * 1 = 2
Add our new value to our running total, we get:
208 + 2 = 210
This = 210, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 210
Our octal notation is now equal to 322
Final Answer
We are done. 210 converted from decimal to octal notation equals 3228.Take the Quiz Switch to Chat Mode
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