Algebra Know-It-ALL

and dividing, it’s almost impossible to get along without zero. In a computer, the numeral 0 is

one of only two possible digits (the other being 1) for building large numerals. In accounting,

the presence or absence of a single 0 on a piece of paper can represent the difference between

the price of a car and the price of a house.

Are you confused?

Let’s write down all the counting numbers from one to twenty-one as Roman numerals. This will give you

a “feel” for how the symbols are arranged to represent adding-on or taking-away of quantities.

The first three are easy: the symbol I means one, II means two, and III means three. Then for four, we

write IV, meaning that one is taken away from five. Proceeding, V means five, VI means six, VII means

seven, and VIII means eight. To represent nine, we write IX, meaning that one is taken away from ten. Then

going on, X means ten, XI means eleven, XII means twelve, and XIII means thirteen. Now for fourteen, we

write XIV, which means ten with four more added on. Then XV means fifteen, XVI means sixteen, XVII

means seventeen, and XVIII means eighteen. For nineteen, we write XIX, which means ten with nine more

added on. Continuing, we have XX that stands for twenty, and XXI to represent twenty-one.

Here’s a challenge!

Write down some Roman numerals in a table as follows. In the first column, put down the equivalents of

one to nine in steps of one. In a second column, put down the equivalents of ten to ninety in steps of ten.

In a third column, put down the equivalents of one hundred to nine hundred in steps of one hundred. In

a fourth column, put down the equivalents of nine hundred ten to nine hundred ninety in steps of ten.

In a fifth column, put down the equivalents of nine hundred ninety-one to nine hundred ninety-nine in

steps of one.

Solution

Refer to Table 1-1. The first column is farthest to the left, and the fifth column is farthest to the right. For

increasing values in each column, read downward. “Normal” numerals are shown along with their Roman

equivalents for clarification.

Roman Numerals 7

Table 1-1. Some examples of Roman numerals. From this progression, you should be

able to see how the system works for fairly large numbers. You should also begin to

understand why mathematicians abandoned this system centuries ago.

1 = I 10 = X 100 = C 910 = CMX 991 = CMXCI
2 = II 20 = XX 200 = CC 920 = CMXX 992 = CMXCII
3 = III 30 = XXX 300 = CCC 930 = CMXXX 993 = CMXCIII
4 = IV 40 = XL 400 = CD 940 = CMXL 994 = CMXCIV
5 = V 50 = L 500 = D 950 = CML 995 = CMXCV
6 = VI 60 = LX 600 = DC 960 = CMLX 996 = CMXCVI
7 = VII 70 = LXX 700 = DCC 970 = CMLXX 997 = CMXCVII
8 = VIII 80 = LXXX 800 = DCCC 980 = CMLXXX 998 = CMXCVIII
9 = IX 90 = XC 900 = CM 990 = CMXC 999 = CMXCIX