Answer
↓Steps Explained:↓
Convert 152 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 >= 152
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 152
Since 512 is greater than 152, 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 152 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 <= 152, 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 152 is 3
Multiplying this coefficient by our original value, we get: 3 * 8 = 24
Add our new value to our running total, we get:
128 + 24 = 152
This = 152, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 152
Our octal notation is now equal to 23
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 152 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
152 + 1 = 153
This is > 152, so we assign a 0 for this digit.
Our total sum remains the same at 152
Our octal notation is now equal to 230
Final Answer
We are done. 152 converted from decimal to octal notation equals 2308.Take the Quiz Switch to Chat Mode
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