All Numbers in Javascript are 64 bit "double" precision IEE754 floating point.
The largest positive whole number that can therefore be accurately represented is 2^53 - 1. The remaining bits are reserved for the exponent.
Your number is exactly 1024 times larger than that, so loses 3 decimal digits of precision. It simply cannot be represented any more accurately.
In ES6 one can use Number.isSafeInteger( # )
to test a number to see if its within the safe range:
var ThisInt = '9223372036854775808';
console.log( Number.isSafeInteger( parseInt( ThisInt ) ) );
There is also a BigInteger library available which should be able to help, though, and avoid you having to do all the string and bit twiddling yourself.
EDIT 2018/12 there's now a native BigInt
class (and new literal syntax) landed in Chrome and NodeJS.
EDIT 2023/11 the BigInt
class has been supported in all mainstream JS engines since late 2020.