Answer
↓Steps Explained:↓
Convert 142 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 >= 142
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 142
Since 512 is greater than 142, 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 142 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 <= 142, 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 142 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
128 + 8 = 136
This is <= 142, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 136
Our octal notation is now equal to 21
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 142 is 6
Multiplying this coefficient by our original value, we get: 6 * 1 = 6
Add our new value to our running total, we get:
136 + 6 = 142
This = 142, so we assign our outside coefficient of 6 for this digit.
Our new sum becomes 142
Our octal notation is now equal to 216
Final Answer
We are done. 142 converted from decimal to octal notation equals 2168.Take the Quiz Switch to Chat Mode
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