Is floating point math broken?

Question

Consider the following code:<!-- language: lang-js --> 0.1 + 0.2 == 0.3 -> false<!-- language: lang-js --> 0.1 + 0.2 -> 0.30000000000000004 Why do these inaccuracies happen?

Answer 1

In base-10 fractions, those fractions that involve factors of 10 can determined precisely such as 1/2, 1/4 and 1/5, which evaluate to exactly 0.5, 0.25 and 0.2 respectively. Fractions that involve values not factors of 10 cannot such as 1/3 or 1/7; instead they are infinitely repeating decimals.

The same principle is in force with computers except here it is base-2, so there are more values that cannot evaluate to an exact value. As long as you are dealing with integers, computer math is exact, but as soon as you involve decimals, inaccuracy is likely to creep in more often than not.