Answer
↓Steps Explained:↓
Convert 189 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 >= 189
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 189
Since 512 is greater than 189, 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 189 is 2
Multiplying this coefficient by our original value, we get: 2 * 64 = 128
Add our new value to our running total, we get:
0 + 128 = 128
This is <= 189, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 128
Our octal notation is now equal to 2
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 189 is 7
Multiplying this coefficient by our original value, we get: 7 * 8 = 56
Add our new value to our running total, we get:
128 + 56 = 184
This is <= 189, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 184
Our octal notation is now equal to 27
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 189 is 5
Multiplying this coefficient by our original value, we get: 5 * 1 = 5
Add our new value to our running total, we get:
184 + 5 = 189
This = 189, so we assign our outside coefficient of 5 for this digit.
Our new sum becomes 189
Our octal notation is now equal to 275
Final Answer
We are done. 189 converted from decimal to octal notation equals 2758.Take the Quiz
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