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Convert 196 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 >= 196

80 = 1

81 = 8

82 = 64

83 = 512 <--- Stop: This is greater than 196

Since 512 is greater than 196, we use 1 power less as our starting point which equals 2

##### Build octal notation

Work backwards from a power of 2

##### 82 = 64

The highest coefficient less than 7 we can multiply this by to stay under 196 is 3

Multiplying this coefficient by our original value, we get: 3 * 64 = 192

Add our new value to our running total, we get:
0 + 192 = 192

This is <= 196, so we assign our outside coefficient of 3 for this digit.

Our new sum becomes 192

Our octal notation is now equal to 3

##### 81 = 8

The highest coefficient less than 7 we can multiply this by to stay under 196 is 1

Multiplying this coefficient by our original value, we get: 1 * 8 = 8

Add our new value to our running total, we get:
192 + 8 = 200

This is > 196, so we assign a 0 for this digit.

Our total sum remains the same at 192

Our octal notation is now equal to 30

##### 80 = 1

The highest coefficient less than 7 we can multiply this by to stay under 196 is 4

Multiplying this coefficient by our original value, we get: 4 * 1 = 4

Add our new value to our running total, we get:
192 + 4 = 196

This = 196, so we assign our outside coefficient of 4 for this digit.

Our new sum becomes 196

Our octal notation is now equal to 304