As a rule, between any two real numbers, there must be another real number. There is no number between .999… and 1, therefore they are the same, simply two ways of writing the same number. If the kid is the curious type, it might be pretty interesting to point out that numbers are conceptually separate from their representation. Most simply: ½=.5, but there’s also binary or hexadecimal, or even more exotic forms (like p-adic or continued fractions). The numbers themselves sorta “exist” out there in the aether as an abstract object that isn’t exactly tied to our notation.
Maybe more like explaining like you are 9, but I’d go with this:
Pick any number that you want. Is that number less than 1? Then it is easy to show that it is also less than 0.999……. The same is true if the number you choose is greater than 1. If both of those things are true then 1 and 0.999999…. have to be equal.
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