Decimal Notation   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 0.542        4.02        Write down the decimal for three thousandths        five and twenty-one hundredths        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       7                                    100                16             28                              10,000        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 .05        2.1                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 Back to the Math 187A page Back to the Math Department page e-mail Questions and Suggestions