Answer
↓Steps Explained:↓
Convert 100 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 >= 100
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 100
Since 512 is greater than 100, 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 100 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
0 + 64 = 64
This is <= 100, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 64
Our octal notation is now equal to 1
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 100 is 4
Multiplying this coefficient by our original value, we get: 4 * 8 = 32
Add our new value to our running total, we get:
64 + 32 = 96
This is <= 100, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 96
Our octal notation is now equal to 14
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 100 is 4
Multiplying this coefficient by our original value, we get: 4 * 1 = 4
Add our new value to our running total, we get:
96 + 4 = 100
This = 100, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 100
Our octal notation is now equal to 144
Final Answer
We are done. 100 converted from decimal to octal notation equals 1448.Take the Quiz Switch to Chat Mode
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