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        five-hundred forty-two thousandths

    2. 4.02        four and two hundredths

    Write down the decimal for

    1. three thousandths        0.003

    2. five and twenty-one hundredths        5.21

  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          0.07  
                         
         100      

    2.          16            28.0016
       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        1/20

    2. 2.1        2 1/10
             

  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.

 

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