Answer
↓Steps Explained:↓
Convert 175 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 >= 175
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 175
Since 512 is greater than 175, 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 175 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 <= 175, 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 175 is 5
Multiplying this coefficient by our original value, we get: 5 * 8 = 40
Add our new value to our running total, we get:
128 + 40 = 168
This is <= 175, so we assign our outside coefficient of 5 for this digit.
Our new sum becomes 168
Our octal notation is now equal to 25
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 175 is 7
Multiplying this coefficient by our original value, we get: 7 * 1 = 7
Add our new value to our running total, we get:
168 + 7 = 175
This = 175, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 175
Our octal notation is now equal to 257
Final Answer
We are done. 175 converted from decimal to octal notation equals 2578.Take the Quiz
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