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    0.0568

    2. 0.0357 17    0.0021

     

  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.

    4.761

  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  
                      
                  06       
                    6   
                     09   
                       9   
                        03
                          3
                          0

    Exercises

    Divide

    1. 17.25 2.3    7.5

    2. 0.00102 5.1    0.0002

    3. 0.000253 0.0011    0.23
          

     

  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 | 99
    2.00  
                   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 | 2
    06.150  
                   204      
                       215       
                       204   
                          110   
                            END
                
    Now round to the nearest penny.  The cost per person is $6.06.

 



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