In pure mathematics, you can get perfect precision with non-terminating fractions. For example, 0.(6) + 0.(3) = 1 is true. The decimal (or binary) representatio

In pure mathematics, you can get perfect precision with non-terminating fractions. For example, 0.(6) + 0.(3) = 1 is true. The decimal (or binary) representation is just "syntax sugar" for the actual fraction - in this case, 2/3 + 1/3 = 1; or, if you prefer, 10/11 + 1/11 = 1, or 0.(10) + 0.(01) = 1. Note: I'm using a notation for infinitely repeating decimals that I learned in school - 0.(6) means 0.6666666...; 0.(01) means 0.010101010101...