The easy "on-the-spot" solution would be to always send two digits instead of one. So you will always read two digits, if it's a one digit number, send 0 and the number.
For example for 13 you will 1 and 3
for 8 you will send 0 and 8
That solution won't scale well though (if you want to roll a dice of 6 digit numbers

). So you might use some kind of terminator character at the end of each number, which will tell you that the number is complete.
edit: me - dumb*ss

You can simply send your number as a byte

that way you can have up to 255 dice at once. I don't know which language you are using on the computer end so can't really help you there, but when you read the number don't subtract the '0' char and what you'll receive will be the byte you have sent.