As the articles that you've already been pointed to say, computers use a float- binary representation. The number 1/10 does not have an exact representation in base-2 floats, much as 1/3 does not have an exact representation in a base-10 float. Computers can handle this problem by using decimal (BCD = Binary-Coded Decimal) arithmetic, but Perl does not directly expose this type. One pragmatic solution to your problem might be to count using integers, where the integer is the desired number multiplied by 100. Then, each time, calculate the float by casting the integer to a float and dividing it by 100. Because this is done each time, errors do not accumulate. Many database systems employ a variation of this "scaled integer" strategy to handle their currency data type.
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