Mathematica numerical "error" for simple multiplication

0.8048780487804877`+0.3 is an arbitrary-precision number with precision 0.3.

With the parentheses, the 0.3 does not specify the precision, but stands as a number. The second line is equivalent to

0.6 * (0.8048780487804877`+0.3) * 0.8414634146341463`

Because the In[75] is completely different than you think.

0.6*0.8048780487804877`+0.3*0.8414634146341463`
(* 0.406365 *)

0.6*0.8048780487804877` + 0.3*0.8414634146341463`
(* 0.735366 *)

Notice the space in the second example: in your case +0.3 is a specification for precision for tick `

Easier example:

(* in this case it's specification of precision *)
1.2`+30
(* 1.20000000000000000000000000000 *)

(* in this case it's 1.2 with $MachinePrecision, plus 30 *)
1.2` + 30
(* 31.2 *)

It's not hte parentheses; it's the missing whitespace!

There is a tiny difference between the meanings of

 0.8048780487804877`+0.3

0.*10^-1

and

 0.8048780487804877` +0.3

1.10488

We have

 0.8048780487804877`+0.3 == 0.8048780487804877`0.3

and the number behind the backtick denotes the number of significant digits. In particular, no addition is performed during evaluation of in case of 0.8048780487804877`+0.3