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 Decimal Numbers
           Decimals were known by the early Chinese
           during the Tang dynasty 618 - 906 AD.
           During this time they created a positional
           decimal numerical system. In the west the
           Dutch mathematician Simon Stevin (1548-1620)
           is usually credited with advancing the
           concept of decimals.

 Place Value  
           Decimals, like whole numbers are based on
           a place value system of notation. ex. In
           the whole number 123, the 1 has a grater
           value than the 3 because of its location.
           If it were 123 dollars, the 1 would be
           worth 97 dollars more than the 3, just
           due its location.
           Decimals continue this system of place
           value. For ex 34.567. The digits to the
           right of the decimal point are less than
           one. The closer the digit is to the
           decimal point the greater its value.
           For example if we refer to money again
           $27.39. We find that the 3 has a greater
           value than the 9. The 3 has a value of
           $.30 and the 9 represents $.09. Does the
           3 have a  greater value than the 2 in
           this example? The value of each place or
           location from left to right starting
           with the first place to the right of the
           decimal point are in order called tenths,
           hundredths, thousandths, ten thousandths,
           hundred thousandths, millionth, ten
           millionth, ....
            Try these examples:
                 1) 98.54367 write down what place
                    each number is located in.
                                        (click for answer)
                                       (Check the answer for each
                    example before you go on to the
                    next example. If you get the
                    wrong answer STOP and try to
                    understand  where you may your
                    mistake. Then do that problem

                 2) 345.67278 write down what place

                    each number is located in.
                    Check your answer (click for answer)

                         Rules for rounding off decimals:

                               Ex.  34.5672  Round off to the hundredths place.
                                      The 6 is in the hundredths  place. Look at the
                                      digit to the right (which is 7) Is it 5 or more?
                                      Yes.  So we add 1 to the 6  and the number 

                                     34.5672 is rounded off to  34.5700. It is customary to 

                                     drop the zeros,  so the answer is 34.57
                               1. Locate the place you want to round off  to.
                               2. Look at the first digit to the right of the place you
                                   are rounding off to.
                               3. If this digit to the right is 5 or more add 1 to the
                                   digit in the rounded  off place and change all of
                                   the digits to the right to zero.
                               4. If the digit to the  right  is less than 5, change
                                   all of these digits  to the right to zero and don't
                                   alter the digit in the place being rounded off too.
                                   Let us  clarify this with an example.
                                Ex.  45.67389  Round off to the hundredths place.
                                       7 is the digit in the hundredths place and 3 is
                                       the first number to the right. Since 3 is less than
                                       5,   45.67389 rounds off to 45.67000 or the
                                       preferred 45.67

              1.  round off to the hundredths place 378.9764  click for answer
              2.  round off to the tenths place     5.739    click for answer
              3.  round off to the thousandths place  45.9995   click for answer