I've been over the Documentation and I read this.
"When you type in an integer like 7, Mathematica assumes that it is exact. If you type in a number like 4.5, with an explicit decimal point, Mathematica assumes that it is accurate only to a fixed number of decimal places."
In other words, it assigns machine precision to the number.
"If you want Mathematica to assume that the argument [0.142] is exactly 142/1000, then you have to say so explicitly."
Is there any way at all to modify this behavior? I would love to be able to type "Sqrt[2.2]" and get "Sqrt[11/5]" for output, or even just "Sqrt[2.2]" for output. As it stands, Mathematica gives me "1.48324". I don't want it to assume that numbers with explicit decimal points have finite precision.
I realize that I can just type out each decimal number as a fraction, but this is a hassle and there should be a way around that.
In fact, it would also be great if FullSimplify and similar functions would take advantage of simple decimal representations. For example, "FullSimplify[617239876987536847/100000000000]" would produce "6172398.76987536847".