##EDIT

Actually, the previous code I gave in **1/** to round numbers is not exactly rounding the numbers ... , it is just removing all the digits that are not "needed". For example `myround[1.3458,3]`returns `1.345` instead of `1.346` !

Anyway, I just found out a much simpler solution :

###0/

- Use for example `Round[number, 10^-3]` instead of `Round[number, 0.001]` to prevent from getting the "extraneous digits" that appear when you copy/paste.

-  As before, use `InputForm` in order to suppress the `NumberMarks` when you copy/paste

For example, concerning the extraneous digits, compare :


    InputForm@N[Round[#, 10^-3] & /@ RandomReal[{1, 10}, 100]] 


with


    InputForm@N[Round[#, 0.001] & /@ RandomReal[{1, 10}, 100]]


=======================================================================
###PREVIOUS

Is this working for you ?

###1/
This code will produce exactly a real with at most n digits to the right of the decimal point  :

    myround[x_, n_] := IntegerPart[x] + IntegerPart[10^n*FractionalPart[x]]/10^n

then

    InputForm[N@(myround[#, 3] & /@ RandomReal[{1, 10}, 10])]


where `InputForm` makes it possible to copy/paste the output without  the `NumberMarks` following each real.

It seems there is no problem also to copy/paste the output of :


    InputForm[
     N@(myround[#, 3] & /@ 
        RandomVariate[
         MultinormalDistribution[{-1.5, 0}, {{2, 0}, {0, 1}}], {10}])]


###2/

Whenever you need to remove [`NumberMarks`](http://reference.wolfram.com/language/ref/NumberMarks.html) you can run for example :

    InputForm[{8.953`, 4.801`, 8.098`, 5.558`, 1.856`, 8.602`, 9.468`, 4.458`,
     4.538`, 3.348`}, NumberMarks->False]

> {8.953, 4.801, 8.098, 5.558, 1.856, 8.602, 9.468, 4.458, 4.538, 3.348}

which can be copied then pasted without the `NumberMarks`.