Use 1, not 2.
js> 2.3 % 1
0.2999999999999998
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» npm install decimal.js
As their author, I recommend bignumber.js or big.js, 'a small, fast Javascript library for arbitrary-precision arithmetic with decimal numbers'.
For a more mature library, the ICU4J BigDecimal translation is also recommended.
There's been a "port" of the Java BigDecimal class (I think it's here: http://freshmeat.net/projects/js_bigdecimal/ ) for a long time. I looked at it a long time ago and it seemed kind-of cumbersome and huge, but (if that's the one I'm thinking of) it's been used as part of some cryptography tools so there's a decent chance that it works OK.
Because cryptography is a likely area to generate a need for such things, that's a good way to snoop around for such packages.
edit: Thanks @Daniel (comment to question) for this older SO question: https://stackoverflow.com/questions/744099/javascript-bigdecimal-library
It is often recommended1 to handle money as an integer representing the number of cents: 2572 cents instead of 25.72 dollars. This is to avoid the problems with floating-point arithmetic that you mention. Fortunately integer arithmetic in floating point is exact, so decimal representation errors can be avoided by scaling.
1Douglas Crockford: JavaScript: The Good Parts: Appendix A - Awful Parts (page 105).
Javascript does have floating point support. But anyway, for financial records, the simplest implementation would simply be storing your values in standard integers. You may either declare an integer to represent the amount in cents, or two integers one for dollars and one for cents.
So $18.57 would become 1857cents in the first technique or 18 dollars and 57 cents in the second.
This has the added advantage of being completely accurate, as integers are stored purely as unique binary representation, there would be no such thing as rounding errors.