Convert 100 from decimal to Base 5
(base 5) notation:
Raise our base of 5 to a power
Start at 0 and increasing by 1 until it is >= 100
50 = 1
51 = 5
52 = 25
53 = 125 <--- Stop: This is greater than 100
Since 125 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 4 we can multiply this by to stay under 100 is 4
Multiplying this coefficient by our original value, we get: 4 * 25 = 100
Add our new value to our running total, we get:
0 + 100 = 100
This = 100, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 100
Our Base 5 notation is now equal to 4
The highest coefficient less than 4 we can multiply this by to stay under 100 is 1
Multiplying this coefficient by our original value, we get: 1 * 5 = 5
Add our new value to our running total, we get:
100 + 5 = 105
This is > 100, so we assign a 0 for this digit.
Our total sum remains the same at 100
Our Base 5 notation is now equal to 40
The highest coefficient less than 4 we can multiply this by to stay under 100 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
100 + 1 = 101
This is > 100, so we assign a 0 for this digit.
Our total sum remains the same at 100
Our Base 5 notation is now equal to 400