No such thing as a small change  
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Strictly, it's not because it's floating point, it's because it's binary floating point. When decimal 1.51 is converted to a binary fraction the result is: 1.1000_0010_1000_1111_0101_1100_0010_1000_1111_0101_1100_0010_1000_1111_0101_1100_0010_1000_1111_0101...which you can see is a repeating binary fraction. As you say, most decimal fractions are like this... so before any errors can be introduced by rounding and what not, most decimal fractions have a builtin "representation" error. Most of the time you won't see the "representation" error, because conversion back to decimal rounds it off. This can lead to bafflement when two values look the same when printed out, but fail $x == $y. Addition and subtraction are the more difficult floating point operations, so you're more likely to see the problems there. Consider: which gives: 0.0900000000000001 0.84  0.34 == 0.5 but != 0.5it really makes me wonder why we persist in using binary floating point for decimal arithmetic ! In reply to Re^4: How can I calculate the right combination of postage stamps?
by gone2015

