Division of Decimals

1. Dividing a Decimal by a Whole Number
   
   Dividing a decimal by a whole number is similar to dividing whole numbers.  One must only be sure to line up the decimal point of the dividend with that of the quotient.  
   
   Example
   
   Divide     143.22 ÷ 6
   
   
   Solution
   
                  23.87
           6 | 143.22  
                12        Hence  143.22 ÷ 6  =  23.87
   
   
   
   Example
   
   Divide     41.472 ÷ 12
   
   
   Solution
   
                  .456
           12 | .472  
                  36      Hence  41.472 ÷ 12   =  3.456
   
   Exercises
   
   Divide
   
   1. 0.4544 ÷ 8   
      
      
   2. 0.0357 ÷ 17   
      
      

    

2. Dividing and Rounding Decimals
   
   Typically division problems yield remainders.  When this is the case we usually do not write the quotient as a mix of decimal and fraction but rather round to an indicated decimal place.  Since rounding involves looking at the digit to the right, we need to find this digit when we do this division.  If necessary, we pad the number with zeros to the right.
   
   Example
   
   Divide and round to the nearest hundredth.
   
           3.64 ÷ 7
   
   Solution
   
   Since we need to round to the nearest hundredth, we will need to see the thousandths digit.  We rewrite
   
           3.650 ÷ 7
   
   
                0.521
           7 | 3.650  
                35        
                  15       
                  14   
                    10   
                    7   
                   END HERE
   
   Since  1 < 5 we do not round up, hence our answer is 0.52
   
   Exercise
   
   Divide  52.37 ÷ 11  and round to the nearest thousandth.
   
   
   
   
3. Dividing a Decimal by a Decimal
   
   Yes Tashia, we finally get to move the decimals around.  
   
   To divide a decimal by a decimal, we move each decimal point to the right until the divisor becomes a whole number.  We may need to pad the dividend with extra zeros first.
   
   Example
   
   Divide  6.693 ÷ 0.3  
   
   Solution
   
   Since the divisor 0.3 has one digit to the right of the decimal we move both decimals one place to the right
   
           66.93 ÷ 3  
   
   Now the divisor is a whole number.  We divide
   
                22.31
           3 | 66.93  
                6      
                 06       
                   6   
                    09   
                      9   
                       03
                         3
                         0
   
   Exercises
   
   Divide
   
   
   1. 17.25 ÷ 2.3   
      
      
   2. 0.00102 ÷ 5.1   
      
      
   3. 0.000253 ÷ 0.0011   
          

    

4. Applications
   
   Example
   
   You have driven 99.2 miles on your recent trip to Sacramento.  If your car used 7.1 gallons, what was your gas mileage?  Round your answer to the nearest tenth.
   
   
   Solution 
   
   This is a division problem since dividing miles by gallons gives miles per gallon.
   
                    13.97
           71 | 992.00  
                  71      
                  282       
                  213   
                    690   
                    639   
                       510
                      END
   
   Now round to the nearest tenth.  Your car got 14.0 miles to the gallon.  
                    
   
   Example 
   
   You are planning an event that will cost a total of $206.15 for 34 attendees.  What is the cost per attendee?
   
   Solution
   
   This is a division problem
   
                      6.063
           34 | 206.150  
                  204      
                      215       
                      204   
                         110   
                           END
               
   Now round to the nearest penny.  The cost per person is $6.06.

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