Question 855645
2.27 express the repeating number as a quotient of two integers
<pre>
I assume you mean 2.272727272727···

let 

  x = 2.272727272727···  write the repeating digits several times:

Multiply that equation by 100 put the one above under it, and
subtract:

100x = 227.2727272727··· 
   x =   2.272727272727···
------------------------
 99x = 225 the repeating decimals cancel out when you subtract them.

  x = 225/99 which reduces to 25/11

Answer 25/11:

Checking:
       <u>  2.2727</u>···
     11)25.0000···
        <u>22</u>
         3 0
         <u>2 2</u>
           80
           <u>77</u>
            30
            <u>22</u>
             80     
             <u>77</u>
              3···

Edwin</pre>