Convert 100 from decimal to Base 7
(base 7) notation:
Raise our base of 7 to a power
Start at 0 and increasing by 1 until it is >= 100
70 = 1
71 = 7
72 = 49
73 = 343 <--- Stop: This is greater than 100
Since 343 is greater than 100, we use 1 power less as our starting point which equals 2
Work backwards from a power of 2
We start with a total sum of 0:
The highest coefficient less than 6 we can multiply this by to stay under 100 is 2
Multiplying this coefficient by our original value, we get: 2 * 49 = 98
Add our new value to our running total, we get:
0 + 98 = 98
This is <= 100, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 98
Our Base 7 notation is now equal to 2
The highest coefficient less than 6 we can multiply this by to stay under 100 is 1
Multiplying this coefficient by our original value, we get: 1 * 7 = 7
Add our new value to our running total, we get:
98 + 7 = 105
This is > 100, so we assign a 0 for this digit.
Our total sum remains the same at 98
Our Base 7 notation is now equal to 20
The highest coefficient less than 6 we can multiply this by to stay under 100 is 2
Multiplying this coefficient by our original value, we get: 2 * 1 = 2
Add our new value to our running total, we get:
98 + 2 = 100
This = 100, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 100
Our Base 7 notation is now equal to 202