Arabic Numerals

Arabic numerals, Arabic Notation, or Indian Notation, was introduced into Europe by the Arabs, by whom is was supposed to have been invented. Investigations have shown that it was adopted by them over 700 years ago, and it has been in use by the residents of India for more than 2000 years. From this latter fact it is sometimes called the Indian Notation.

The system employs ten characters or figures to express numbers. The first character, called zero, the cipher, the naught, and nothing, has no value of its own. The other nine characters are called significant figures, because each has a value of its own. The significant figures are called digits, a word derived from the Latin term digitus, which signifies finger. The ten Arabic characters are the alphabet of arithmetic, and by combining them according to certain principles, all numbers can be expressed. We will now examine the most important of these principles. Fractional and decimal notation and the notation of compound numbers will be discussed in their appropriate places. Each of the nine digits has a value of its own; hence, any number not greater than 9 can be expressed by one figure.

As there is no single character to represnt ten, we express it by writing the digit, 1, to the left of the zero, 0, thus, 10. In the same manner we represent 20, 30, 40, 50, 60, 70, 80, and 90. When a number is expressd by two figures, the right figure is called units, and the left figure is called tens. We express the numbers between 10 and 20 by writing 1 in the place of the tens, with each of the digits respectively in the place of the units. Thus, 11, 12, 13, 14, 15, 16, 17, 18, and 19. In like manner, we express the numbers between 20 and 30 and any two consecutive tens. Tus, 21, 22, 23, 24, 25, 26, 27, 28, 29, 34, 56, 72, and 93. The greatest number that can be expressed with two figures is 99.

We express the number one hundred by writing the digit 1 at the left of two zeros, thus 100. In like manner, we write two hundred as 200, three hundred as 300, four hundred as 400, five hundred as 500, six hundred as 600, seven hundred as 700, eight hundred as 800, and nine hundred as 900.When a number is expressed by three figures, the figure on the right is called the units, the middle figure is called the tens, and the left figure is called the hundreds. As the zero has no value, they are used to denote the absence of value in the places they occupy. We express ones, ten, hundreds, etc. by writing digits in the place of the zeros. To express one hundred fifty, we write 1 in the hundreds place, 5 in the tens place, and zero in the units place, thus 150. To express seven hundred ninety-two, we write 7 in the hundreds place, 9 in the tens place, and 2 in the ones place, thus 192. The greatest number that can be expressed by three figures is 999.

Continue with thousands, ten thousands, hundred thousands, millions, billions, trillions, quadrillions, quintillions, sextillions, septillions, octilions, etc.

Each place can be called an order units=1st order, tens=2nd order, hundreds=3rd order, etc.

From the foregoing explanations, several important principles are derived, which we will now present.

1. Figures have two values, simple and local. The simple value is the value of the figure alone; thus, 2, 5, 8. Local value is the value of a figure when it is used with another figure or figures in the same number. Thus, in 842, the simple values are 8, 4, and 2; but the local values are 800, 40, and 2. When a figure occupies the unit's place, its simple and local values are the same.

2. A digit or figure, if used in the second place expresses tens, in the third place hundreds, in the fourth place, thousands, and so on.

3. As 10 units make 1 ten, 10 tens make 100, 10 hundreds make 1000, and ten units of any order or in any place, make one unit of the next higher order, or in the next place at the left, we readily see that the Arabic method is based on the following two laws.

Two General Laws I. The value of the different orders increases from right to left, and decreases from left to right, in a tenfold ratio.

II. Every addition of a figure to a number increases the local value of a digit tenfold; and every removal of a figure from the number diminishes the digit's local value tenfold.