Page 17 - Appplied Mathematics for the Petroleum and Other Industries, 5th Edition

2 THE NUMBER SYSTEM

onto the wall of a shelter to record a count. But, as time passed and humans
became more sophisticated, they found that they had to keep track of large
numbers. Indeed, these numbers were so large that using fingers and scratching
straight lines was not adequate. So, they came up with special symbols, or figures,
to represent numbers. A group of people who lived in the Middle East—the
Arabs—cleverly invented symbols to represent the numbers from one to nine
and for zero. Having a figure for zero was a great step forward, as you will see
in a moment. Because the Arabs were the first to create symbols for numbers,
everyone began calling the symbols Arabic numerals.
Later, the Romans also developed a system of symbols, which, logically
enough, were called Roman numerals. Today, we mostly use Arabic numerals;
however, we sometimes use Roman numerals for such items as chapter headings
in books, hours on clocks, and copyright dates for movies.
The Arabic figures are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Letters of the alphabet
stand for Roman numerals. For example, the Roman numeral I represents the
Arabic numeral 1. Similarly, the Roman V is equivalent to the Arabic 5, X is
10, L is 50, C is 100, D is 500, and M is 1,000. Table 1.1 lists several Arabic
numerals and their Roman equivalents.
Notice that the Roman numeral system sometimes places a symbol of lower
TABLE 1.1 value before the symbol for the next higher value. This placement indicates that
Arabic Numerals and you should subtract the lower value from the higher value. For example, the Ro-
Roman Equivalents man numeral for 4 is IV, instead of IIII. The I before the V means to subtract 1
from 5. Similarly, the Roman numeral for 9 is IX and the Roman numeral for 49
Arabic Roman is XLIX. For the equivalent of 9, the I before the X means subtract 1 from ten.
For 49, the X before the L means to subtract 10 from 50, which is L, and the
1 I I means subtract 1 from 10, which is 9. Therefore, Arabic 49 is Roman XLIX.
2 II Notice, too, that the Roman system does not have a symbol for zero.
Suppose a movie was copyrighted in 1969. The Roman numeral equivalent
3 III
is MCMLXIX. M equals 1,000; C (100) less M (1,000) is 900; LX is 60; and IX
4 IV
is 9. On the other hand, the Roman numeral equivalent for a movie copyrighted
5 V
in 2000 is simply MM.
9 IX Because the Arabic system contains the figures 0 through 9, it certainly
10 X saves time in writing—that is, Arabic 3 is easier to write than Roman III. But this
19 XIX advantage is only a minor part of the system’s usefulness. The truly revolutionary
20 XX aspect of the Arabic system is that the placement of each symbol determines its
value. That is, Arabic numerals are written one after the other on a single line
40 XL
and their place in that line indicates the number’s value.
44 XLIV
Take, for example, the number 692. Because we read from left to right,
45 XLV
six starts the number, nine follows it, and two follows the nine. The number’s
49 XLIX position, or place, in the line determines the value of that number. In this case,
50 L the position of the six represents 600, or six hundreds; the nine represents 90,
90 XC or ten nines; and the two represents two ones. Consequently, we read it as six
100 C hundred ninety-two—that is, the number contains six hundreds, nine tens,
Petroleum Extension-The University of Texas at Austin
500 D and two ones.
Another feature of Arabic numbers is that we can put different numbers in
700 DCC
columns and manipulate them in many ways. For example, as you will soon learn,
900 CM
several numbers can be added together, subtracted from each other, multiplied
999 CMIX by each other, and divided by each other.
1,000 M Table 1.2 shows four Arabic numerals arranged in columns. The numbers
1,500 MD are 5, 50, 500, and 5,000. Reading from left to right and starting in the table’s
first row, the table displays these numbers as 0005, 0050, 0500, and 5,000 to show