How to increment the number in a string while keeping the appropriate trailing/leading zeros

I'm curious as to how accounting softwares enable incrementing "invoice number" ie from INV-001 increments to INV-002. Let's dissect by only focusing on "001".

I've done some "Googling" and found the use of "%03d":

puts "%03d" % 1#=> "001"

That's a start, but I struggle with many variations:

str = "001"str = "009"

At school we were taught:

# Let's assume we knew nothing about strings001 + 1 # gives us 002. How?# This is what really happens##  001# +  1# ______#  002

Using the above, if we "add" 009 + 1, we get 010 if we use the above method.

Things are much different with programming as converting "001" to integer becomes 1.

How can I create a method that knows how to add "001" plus 1 which returns "002"?

I assume a lot of things are going on with the above formula:

1. How it knows what to add 1 to.
2. How it knows to bring the "remainder" to the left then add ie 009 + 1 = 010
3. For 3, how it knows to keep a zero at the end 010 and not 10

I've tried many things but are all incorrect. Basically I need to increment the strings:

# Result should be when str is incremented by 1str = "002"+ 1 #=> "003"str = "0002"+ 1 #=> "0003"str = "009"+ 1 #=> "010"str = "0002"+ 1 #=> "0010"str = "02"+ 1 #=> "03"str = "1"+ 1 #=> "2"

Converting the str to float loses the zeros and I cant seem to use any logic successfully with "%03d".