How do I explain repeating decimals to a child?

By "repeating", do you mean "recurring" (the only term I have ever seen for values like 0.33333.....)?

If so perhaps the easiest way is by a division (hard to represent in a very basic text editor not set up to represent arithmetic):

3[u])1.00000000[/u]

3 into 1 won't go so carry 1:

3 [u])0.10[/u] = 0.3 remainder 0.01 so carry 1:

3[u])0.310[/u]...
0.33....

And so on, if that survives being posted!

Use apples, so 10 apples is 10 decimals. 8 apples is 8 of 10 decimals, and so on.

Have his teacher

ASŤ

Use a long division example, e.g. 2 / 3. You really [i]feel[/i] what it represents doing long division.