One way to introduce the idea that a number represented as decimal digits can have multiple representations is to talk about the numbers 1 and 1.0 being exactly the same. And that 1.00 is the same as 1. Just like 0, 0.0, and 0.00 are the same number. Most people would agree at this point.

Then keep stretching the number of zeroes to 0.000... - which, again, is exactly the same as 0.

From there, it is not a huge stretch to be able to go from that 0.000... is another way to write 0, then 0.999... is another way to write 1.