1. ARITHMETIC is the science of numbers. 2. Numbers express how many units, or parts of a unit, there are in any quantity.

3. Quantity is any thing that can be increased, diminished, or measured.

4. The least whole number employed to express or measure quantity of the same kind is called a unit. 5. A number expressing a particular kind of a unit is called a concrete number; as, 1 dollar, 2 books, &c.

6. When a number does not express any particular kind of a unit, it is called an abstract number; as, 1, 4, 7, &c.

OBS. 1. Concrete numbers are also called denominate or compound numbers.

OBS. 2. Whole numbers are sometimes called integers.

7. In the computation of numbers, ten characters are employed, called figures; thus: 1, one; 2, two; 3,

What is arithmetic ? What are numbers? What is quantity? What is a unit? What is a concrete number? What is an abstract number?

three; 4, four; 5, five; 6, six; 7, seven; 8, eight; 9, nine; 0, cipher. The first nine figures are called significant, because they have a given value assigned them. The cipher has no representative value, but is used where no number is to be expressed.

OBS. 1. By the aid of these ten characters any possible or conceivable quantity may be expressed.

OBS. 2. The first nine figures are sometimes called digits, from the Latin word digitus, signifying a finger.

8. The various operations of arithmetic are performed by NUMERATION, ADDITION, MULTIPLICATION, SUBTRACTION, and DIVISION.

Addition and multiplication are employed to show how numbers may be increased; subtraction and division how they may be diminished.

NUMERATION.

SECTION II.

9. NUMERATION is the art of expressing any number whatever by figures.

Figures are arranged in different orders or places, and have different values assigned them, according to the place they occupy. The first place, which is always at the right, represents units; the second, tens; the third, hundreds; the fourth, thousands; the fifth, tens of thousands; the sixth, hundreds of thousands ; the seventh, millions, &c. Thus the figure 1 represents a unit, a ten, a hundred, a thousand, &c., according to the place it occupies. In all places in which no number is to be expressed, ciphers must be written.

Which are significant figures? How are the various operatións of arithmetic performed? What is numeration? How are figures arranged? What does the first place represent? The second? The third? The fourth? The fifth? &c. When must ciphers be used?