The correct answer is:
[C]: "
" .
_____________________________________________________
<span>
Explanation:_____________________________________________________</span>
Let us begin by converting the:
"0.42 (with the "repeating bar on the digits, "42") " ;
into a fraction, as follows:
______________________________________________________ Let x = 0.42424242424242424242424242424242....
100x = 42.42424242424242424242424242424242....
______________________________________________________
100x = 42.42424242424242424242424242424242....
– x = 0.42424242424242424242424242424242...
______________________________________________________
99x = 42.000000000000000000000000000000.... ;
→ 99x = 42 ;
Divide each side of the equation by " 99 " ;
to isolate "x" on one side of the equation; & to solve for "x" ;
______________________________________________________ → 99x / 99 = 42/99 = (42 ÷ 3) / (99 ÷ 3) = 14/ 33;
→ x = "
" .
So; "0.42 (with a repeating bar over the digits, "42" ;
is equal to: "
"
________________________________________________ So, rewrite the question/problem being asked:
________________________________________________ "Find the quotient:
________________________________________________ ÷
;
=
*
;
Note: The "14" cancels to a "7" <span>; and</span> the "2" cancels to a "1" ;
→ {since: " 14 ÷ 2 = 7 " ; and since: " 2 ÷ 2 = 1 "} ;
Note : The "33" cancels to an "11" ; and the "9" cancels to a "3" ;
→ {since: " 33 ÷ 3 = 11 " ; and since: " 9 ÷ 3 = 3 "} ;
And we can rewrite the problem as:
____________________________________________________ "
*
" ;
=
=
;
→ which is:
Answer choice: [C]: "
" .
____________________________________________________
