I had to check but yeah, that's true, the ECMA spec even says explicitly in its intro: "JSON is agnostic about numbers", they are "only a sequence of digits".
(Unrelated observation from looking at the spec again: there's no standard/recommended decoding behaviour if an object has several members with the same key.)
I don't think JSON requires the number representation to be double-precision, that can be up to the parser to decide how to represent a number. I think most people misrepresent this because the number implementation in JavaScript is double-precision, but that's not necessarily true for JSON. Am I wrong about that? Does JSON require the number format to be double-precision?