Convert 125 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 >= 125
70 = 1
71 = 7
72 = 49
73 = 343 <--- Stop: This is greater than 125
Since 343 is greater than 125, 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 125 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 <= 125, 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 125 is 3
Multiplying this coefficient by our original value, we get: 3 * 7 = 21
Add our new value to our running total, we get:
98 + 21 = 119
This is <= 125, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 119
Our Base 7 notation is now equal to 23
The highest coefficient less than 6 we can multiply this by to stay under 125 is 6
Multiplying this coefficient by our original value, we get: 6 * 1 = 6
Add our new value to our running total, we get:
119 + 6 = 125
This = 125, so we assign our outside coefficient of 6 for this digit.
Our new sum becomes 125
Our Base 7 notation is now equal to 236