FRACTION TO DECIMAL

To convert fractions to decimals we just divide.  The only catch is when should we stop.  Sometimes we end when there is no remainder.
Example: Convert the fraction 3/8 to a decimal.

Solution

             0.375
        8 | 3
.000  
             24        
               60       
               56   
                 40   
                 40
                   0
Hence    

             3
                   =  0.375                 
             8

Other times the digit repeats itself

Example: Convert the fraction 5/6 to a decimal.

Solution

             0.833
        6 | 5
.000  
             48        
               20       
               18   
                 20   
                 18
                   20

We see that if we keep working it out we will continually get 3.  That is 
    

             5
                   =  0.833333...                 
             6

We put a bar over the 3 to indicate that the 3 repeats.

0.83333...  =  0.83 


Example: Convert the fraction 4 2/7 to a decimal.

Solution: Divide only the fractional part

             0.285714
        7 | 2
.00000000  
             14        
               60       
               56   
                 40   
                 35
                   50
                   49
                     10
                       7
                       30
                       28
                         20                
We are back to where we began.

Hence 
 
               2
         4          =  4
.285714
               7
Notice the 4 from the mixed number is the whole number part.             
Example: Fill in the green blank with "<" , ">", or "="

           2
                
                   0.133
          15           

Solution


We first convert the fraction into a decimal.  Then compare.  We will need to divide until we recognize a difference or recognize equality

              0.13
        15 | 2
.00 
 
               15        
                 50       
                 45   
                    50   

We see that this is the repeating decimal 


        0.13   =  0.133333... 

Now notice that 

        0.133 = 0.133000000... < 0.1333333...
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