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Decimal Notation

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    Decimal Notation

     

    1. Naming a Decimal

      Among all fractions there is a collection of special fractions called decimal fractions.  Decimal fractions are fractions where the denominator is a power of ten.  For example

               3             78                 91            142
                    ,                 ,                      ,                      
              10           100            10,000        1,000


      There is an alternative way to write a decimal fraction.  We can write

            3                       78                        91
                    =  0.3,               =  0.78,                   =  0.0091                                    
           10                     100                    10,000


      Notice that the the decimal place is moved to the left the same number of digits as number of zeros in the denominator.

      To read decimal numbers remember that from left to right the digits to the right of the decimal point are:

              Tenths, Hundredths, Thousandths, Ten-Thousandths, etc.



      Examples

      0.23  =  twenty-three hundredths

      5.2  =  five and two tenths   We use the word "and" to separate the whole number and decimal

      34.00021  =  thirty-four and twenty-one hundred-thousandths  



      Exercises

      Write down the word for

      1. 0.542        
         

      2. 4.02        
         

      Write down the decimal for
       

      1. three thousandths        

      2. five and twenty-one hundredths        
         

    2. Changing From Fractions to Decimals

      To change a fraction to a decimal, we count the number of zeros in the denominator.  This number is the number of digits to the right of the decimal place.

      Examples

          3                        59                         5
                   =  0.3 ,               =  0.59,                 =   0.005                
         10                      100                     1,000



            17                                    8              
       4             =  4.17 ,      93                =  93.008            
           100                                1000                   




      Exercises

      Write the decimal form of 
       

      1.      7            
                           
           100      

         

      2.          16            
         28                      
               10,000    
          

         

    3. Converting Decimals to Fractions

      To convert a decimal to a fraction, we put the decimal part, we count the number of digits to the left of the decimal place.  Then we place the left of the decimal over 1 with this many zeros.  Finally reduce if possible

      Examples

                    2 4          2              
        0.4  =           =                    
                    
      510         5           


                         
      1155              11              
        3.55  = 3                =  3                    
                        
      20100              20    

      Exercises

      Convert the following decimals to fractions
       

      1. .05        
         

      2. 2.1        
               
         

    4. Application

      A stream that feeds into Lake Tahoe was found to contain a concentration of 25 parts per million of MTBE.  What fraction represents the concentration of MTBE in the stream?

      Solution

      23 parts per million is 23 out of 1,000,000 or

                    25                             1
                                      =                         
              1,000,000                  40,000


      The concentration of MTBE is 1/40,000.

     



    Back to the Decimals page

     

     

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