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##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 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.