Readings for Session 6 – Place Value
You contracted for a job to be paid
and were to be paid $9,100 when the job was completed. The
person wrote you a check made out for $1,900. Would you overlook
the mistake since the person’s only mistake was to transpose two
digits? If not, why would you want the person to write a
different check?
You would probably not accept the
check because the interchanging of the two digits would be a
huge change in the amount of money paid. In our numeral system
(the Hindu-Arabic numeration system), the position of the
numerals is important. The
Hindu-Arabic numeration system is a
place-value system,
which means that the position of the numerals affects the value
of the number it represents. (Remember that a numeral is the
symbol and that a number is the value a numeral represents.) In
the situation above, the 9 in the $9,100 represents nine
thousand dollars and the 1 represents one hundred dollars.
In $1,900, the 9 represents nine hundred dollars and the
1 represents one thousand dollars.
Notice the close relationship the
place-value system has to sets, cardinality, and the set
operation of union. The amount of money represented by $9,100
may be thought of as the cardinality of the union of a set
containing nine thousand dollars with a set containing one
hundred dollars. Similarly, the amount of money represented by
$1,900 may be thought of as the cardinality of the union of a
set containing one thousand dollars with a set containing nine
hundred dollars.
The Hindu’s developed the system
before the 9th century. The Persian mathematician
al-Khwarizmi wrote a book on the system in about 825 A.D.
after which the system was adopted by the Arabs. Though the
system was first introduced into Europe in the 10th
century, it was not widely used in Europe until after the
invention of the printing press in the 15th century.
Return
to Peil's Homepage | Minnesota
State University Moorhead | Mathematics
Department