What is 3 × 100 + 3 × 1 + 4 ×( 1/10) + 5 ×( 1/100) + 7 ×(1/1000) ?
330.457
303.457
33.0457
303.0457

The answer is:  [B]:  " 303.457 " .
Explanation:  Use the "order of operations"; which is represented by the mnemonic device:

PE MD AS ;  (Please excuse my dear Aunt Sally/Susan);

also, known as:  BE MD AS ;  (Be excused, my dear Aunt Sally/Susan);

The operations performed are done in order of first to last;  the "P" stands for parentheses" ;  The "B" stands for "brackets".

The "MD" stands for "multiplication, then division";  As per the mnemonic device, there should be an "arrow from left to right over the "MD" ; which means that when both Multiplication AND division occurs; the operations are perform in order from left to right, as they occur in the problem being solved.

The "AS" stands for "addition, then subtraction".  Again, as per the mnemonic device, there should be an "arrow from left to right over the "AS" ; which means that when both addition AND subtraction occurs; the operations are perform in order from left to right, as they occur in the problem being solved.

We are given: 

3 × 100 + 3 × 1 + 4 ×( 1/10) + 5 ×( 1/100) + 7 ×(1/1000) ?

 Using the "order of operations" ;  we can rewrite this problem as:

(3*100) + (3*1) + [ 4*(1/10) ]  + [5*(1/100) + [7*(1/1000)] ;

Note that both multiplication and division take priority over addition, according to the "order of operations".

Now, rewrite:  300 + 3 + (4/10) + (5/100) + (7/1000).

Change the "(4/10)"  to:   ?/ 1000 ;  "4/10" = (4*100)/(10*100) = 400/1000 ;

Change the "(5/100)" to:  ?/1000 ;  "5/10" = (5*10)/(100*10) = 50/1000  ;


Now, rewrite:   300 + 3 + (4/10) + (5/100) + (7/1000) =

            300 + 3 + (400/1000) + (50/1000) + (7/1000) =

            303 + [ (400 + 50 + 7) / 1000 =    303 + (457/ 1000) ;

                                                          =  303.457 ;
                                                   which is:  Answer choice:  [B].