Solution To Moderate Exercise Number One

MODERATE EXERCISES

(1) Convert ¹¹/₁₃ to decimal form, showing the repeating section.

SOLUTION:

We begin by doing long division, as follows:


      0.846153?   
   _______________
13 ) 11.0000000...
     10 4         
     ____         
        60        
        52        
       ___        
         80       
         78       
        ___       
          20      
          13      
         ___      
           70     
           65     
          ___     
            50    
            39    
           ___    
            110

Note that when we reach the question mark, we have to divide 13 into 110. But that is what we had to do at the very beginning. This means that the digit pattern 846153 will be repeated, and at the end of that string of digits we will have to divide 13 into 110 again. So, in computing ¹¹/₁₃ through long division, the digit pattern 846153 will be repeated over and over.

Thus, ¹¹/₁₃ = 0.______
Thus, ¹¹/₁₃ = 0.846153 .

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