MODERN PRACTICAL ARITHMETIC

NOTATION AND NUMERATION

1. A unit is a single thing of any kind; as one, one apple, one dollar, one pound.

A number consists of one or more units; as one, five, seven cents, nine men.

Arithmetic is the science that treats of numbers and the methods of using them.

Numbers may be expressed by words, by figures, or by letters.

A system of notation is a method of expressing numbers by figures or by letters.

Two systems of notation are in use, the Arabic and the Roman. The Arabic system is used in all our arithmetical calculations.

THE ARABIC SYSTEM OF NOTATION

2. To express numbers, the Arabic notation employs ten characters, called figures; namely, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. The first nine numbers are represented by the first nine figures, and all the other numbers by combinations of the ten figures.

NOTE. The Arabic system of notation was so called because its characters were supposed to have been introduced into Europe by the Arabians; but it is now generally acknowledged that they originated in India. It is also called the decimal system and the common system.

The order of a figure is the place it occupies in a number.

Units of the first order, or units

3. A unit or single thing is one,
One unit and one more are two,
Two units and one more are three,

written 1.

written 2.

written 3.
written 4.
written 5.
written 6.

Three units and one more are four,
Four units and one more are five,
Five units and one more are six,
Six units and one more are seven, written 7.
Seven units and one more are eight, written 8.
Eight units and one more are nine, written 9.

These nine characters are called significant figures, because they denote something.

The character 0, called naught, cipher, or zero, stands for nothing; its use is to fill vacant orders.

When a figure stands alone or in the first place at the right of a number, it represents one or more units of the first order. Units of the first order are called simply units; and the place they occupy is called the units' place.

Units of the second order, or tens

Ten is

4. Nine units and one more are called ten. represented also by the figure 1 written in the second place from the right and 0 in the units' place.

When a figure in a number stands in the second place from the right, it represents one or more units of the second order.

Units of the second order are called tens; and the place they occupy is called the tens' place.

Tens and units

5. The numbers between 10 and 20, 20 and 30, etc., are expressed by representing the tens and units of which they are composed.

1. Twenty-three; twenty-four; twenty-five; twentysix; twenty-seven; twenty-eight; twenty-nine.

2. Thirty-seven; forty-two; fifty-six; sixty-nine; seventy-three; eighty-seven; ninety-four.

3. Eighty-three; forty-five; ninety-nine; fifty-one; thirty-six; seventy-eight; sixty-two.

4. Fifty-five; ninety-three; eighty-one; sixty-seven; forty-nine; seventy-four; thirty-eight.

5. Seventy-six; forty-four; eighty-two; fifty-seven; thirty-five; ninety-one; sixty-three.