ARITHMETIC.

PART I.

1. ARITHMETIC teaches about numbers-about the way of writing them down by means of figures, and about the manner of reckoning with them, in the various dealings of people with one another, in the common course of business, and in the different concerns of life.

2. The number one is called unity; and an integer, or whole number, is a collection of ones, unities, or units.

3. NOTATION is the art of writing down any number in figures.

4. The figures 1, 2, 3, 4, 5, 6, 7, 8, 9 are used to express the whole numbers, one, two, three, four, five, six, seven, eight, nine, respectively; and the figure 0 represents nought or nothing.

5. By means of the above ten figures, which are called the nine digits and zero, we are able to express any number whatever.

This is effected thus:

A figure standing by itself, or on the right hand of other figures, is used with its own proper value, to express so many units;

A figure standing in the second place from the right (that is, with one figure after it) is used to express so many tens of units;

A figure standing in the third place from the right (that is, with two figures after it) is used to express so many tens of tens, or hundreds of units;

A figure standing in the fourth place from the right (that is, with three figures after it) is used to express so many tens of hundreds, or thousands of units;

B

-Units.

And so on, according to the following Table, which is

called

971

~ Millions.

Tens of Millions.
Hundreds of Millions.

Hundreds of T. of Millions.

co Thousands of Millions. Tens of T. of Millions.

Billions.

Tens of Billions.

co Hundreds of Billions.

∞ Hundreds of T. of Billions.

-Thousands of Billions.

Tens of T. of Billions.

← &c.

Trillions.

and so on to trillions, quadrillions, &c. if necessary.

6. Let it be noted, then, that the value of any figure is increased ten-fold by its being moved one place to the left.

Thus 7 means seven: but, in 73, the 7 stands for ten times seven, or seventy; in 731, the 7 stands for ten times seventy, or seven hundred; in 7031, the 7 stands for ten times seven hundred, or seven thousand; and

so on.

Ex. Express in figures the following number:-Seven millions four hundred and seventy thousand three hundred and eighteen.

Ans. 7,470,318.

Ex. 1.

EXPRESS in figures the following numbers:

(1.) Twelve, fourteen, nineteen, twenty-seven.
(2.) Thirty, thirty-nine, forty-seven, fifty.
(3.) Sixty-one, seventy, eighty-eight, ninety-two.

(4.) One hundred and one, one hundred and ten, one hundred and thirteen, one hundred and fifty-five.

(5.) Two hundred, two hundred and two, two hundred and twelve, three hundred and thirty.

(6.). Five hundred and seven, six hundred and sixty-three, seven hundred and seventeen, eight hundred and eighty.

(7.) One thousand and one, one thousand and ten, one thousand one hundred, one thousand and eleven.

(8.) One thousand one hundred and one, one thousand one hundred and ten, one thousand one hundred and eleven, one thousand six hundred and five.

(9.) One thousand and seventy, two thousand three hundred and three, three thousand and thirty, four thousand and fourteen.

(10.) Three thousand two hundred and twelve, four thousand one hundred and eighteen, five thousand six hundred and seven, seven thousand one hundred and ninety.

(11.) One thousand six hundred, two thousand and eleven, eight thousand and fifty, nine thousand and one.

(12.) One thousand and fourteen, three thousand, seven thousand and six, eight thousand five hundred and twentythree.

(13.) Twenty thousand, forty-three thousand and fiftynine, sixty-eight thousand and seventy, eighty-nine thousand six hundred and five.

(14.) Sixty-one thousand, seventy thousand and eight, ninety-four thousand six hundred and twenty, thirty thousand two hundred and eleven.

(15.) Thirteen thousand and thirty-one, thirty thousand and thirteen, thirty-one. thousand three hundred and one, fifty-two thousand and seventy-three.

(16.) Seventy-eight thousand and eleven, ninety thousand seven hundred and four, twelve thousand and five, twenty thousand one hundred and two.

(17.) Five hundred thousand and two, six hundred thousand seven hundred and thirteen, eight hundred and ten thousand one hundred and one, nine hundred and five thousand and fifty.

(18.) Three millions five hundred thousand and eighteen, fourteen millions two hundred and seven thousand five hundred and seventy-three, one hundred and seven millions two hundred and four thousand and three, one thousand two hundred and thirty-four millions five hundred and sixtyseven thousand eight hundred and ninety.

7. NUMERATION is the art of reading, or writing down in words, the number which is expressed by any set of figures. Ex. Write down in words the number expressed by 5,402,679. Ans. Five millions four hundred and two thousand six hundred and seventy-nine.

Ex. 2.

Read (or write down) in words the following numbers:

(1.) 10, 13, 17, 23.

(3.) 100, 101, 110, 111.

(5.) 410, 444, 505, 611.

(2.) 35, 40, 55, 73.

(4.) 276, 317, 371, 401. (6.) 717, 880, 909, 971.