In this post, I will explain why Floating-Point numbers are not always precise. First, let me remind us of the basics of Floating-Point representation quickly.
If you are a programmer and handling numbers with fractions (for example to represent an elapsed time[secs] since a certain event or transaction money[dollars]), you might have heard that you should not use Floating-Point types because they are not always accurate/precise.
In this post, I will explain why Floating-Point numbers are not always precise.
First, let me remind us of the basics of Floating-Point representation quickly.
IEEE 754 floating point standard specifies binary representation format of floating point as below,
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In this case, the floating-point value representation has 32 bits size(called single-precision, for the rest of the post, I will focus on the single-precision floating-point). In C or C++ programming language, this corresponds to _float _type on most platforms(C++ standard does not specify the size).
To compute a number from the encoded value, the following form is used.
IEEE 754 adds an invisible leading bit(that is not actually encoded) with value 1 to save more bits in the fraction bits.
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