Problem with very small numbers?

Question

I tried to assign a very small number to a double value, like so:

double verySmall = 0.000000001;

9 fractional digits. For some reason, when I multiplicate this value by 10, I get something like 0.000000007. I slighly remember there were problems writing big numbers like this in plain text into source code. Do I have to wrap it in some function or a directive in order to feed it correctly to the compiler? Or is it fine to type in such small numbers in text?

Answer 1

The problem is with floating point arithmetic not with writing literals in source code. It is not designed to be exact. The best way around is to not use the built in double - use integers only (if possible) with power of 10 coefficients, sum everything up and display the final useful figure after rounding.

Answer 2

As usual, you need to read stuff like this in order to learn more about how floating-point numbers work on computers. You cannot expect to be able to store any random fraction with perfect results, just as you can't expect to store any random integer. There are bits at the bottom, and their numbers are limited.

Answer 3

Standard floating point numbers are not stored in a perfect format, they're stored in a format that's fairly compact and fairly easy to perform math on. They are imprecise at surprisingly small precision levels. But fast. More here.

If you're dealing with very small numbers, you'll want to see if Objective-C or Cocoa provides something analagous to the java.math.BigDecimal class in Java. This is precisely for dealing with numbers where precision is more important than speed. If there isn't one, you may need to port it (the source to BigDecimal is available and fairly straightforward).

EDIT: iKenndac points out the NSDecimalNumber class, which is the analogue for java.math.BigDecimal. No port required.