### 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                   0Hence                 3                   =  0.375                              8Other times the digit repeats itselfExample: Convert the fraction 5/6 to a decimal.Solution             0.833        6 | 5.000               48                       20                      18                    20                    18                   20We see that if we keep working it out we will continually get 3.  That is                  5                   =  0.833333...                              6We 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           SolutionWe 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...