ARITHMETIC.

ARITHMETIC is the art of computing by numbers. It has five principal rules for its operations; viz. numeration, addition, subtraction, multiplication, and division.

NUMERATION.

Numeration teaches to write or express numbers by figures, and to read numbers thus written or expressed.

In treating of numbers, the following terms are employed: viz. unit, ten, hundred, thousand, and mil lion; as also billion, trillion, and some others. But the latter are seldom used.

A unit is a single one.

A ten is ten units.

A hundred is ten tens.

A thousand is ten hundreds.

A million is ten hundred thousands.

Note.-As it takes ten hundred thousands to make a million, when we express a number greater than a thousand, and less than a million, we use tens of thousands, or hundreds of thousands, or both, as the case requires. Likewise, to express a number greater than a million, we employ tens of millions, or hundreds of millions, &c.

The following are the figures used in numeration, with their names above them.

One two three four five six seven eight nine

1

3 4 5 6

8

9

2 17 Each of these figures represents the number which its name denotes; but it is understood to be that number of units, or that number of tens, or that number of hundreds, &c., according to its relative place: which is exemplified in the following tables:

1 1

1, 1 1 1, 1 1 1

2 2 2, 2 2 2, 2 2 2 These tables show that in using figures to express numbers, they are placed in a horizontal row-the first figure at the right hand representing one or more units, the next tens, the next hundreds, &c. Thus a 1 is one unit, or one ten, or one hundred, &c., according to the place in which it stands; and in like manner, a 2 is two units, or two tens, or two hundreds, &c. The same rule determines the value of each of the other figures.

In reading numbers, the units and tens are taken together. 1 ten and 1 unit are read eleven; 1 ten and 2 units, twelve; 1 ten and 3 units, thirteen, &c.: 2 tens and one unit are read twenty-one; 3 tens and 1 unit, thirty-one, &c. Thus the number expressed by the row of figures in table first is read-one hundred and eleven millions, one hundred and eleven thousands, one hundred and eleven. That expressed by the figures in table second is read-two hundred and twenty-two millions, two hundred and twenty-two thousands, two hundred and twenty-two. The succeeding tables will further illustrate the subject.

In writing numbers which have no units, or no tens, or no hundreds, &c., the order observed in the foregoing tables must be maintained by filling the vacant places with a character called a nought or cypher, (0) which, of itself, represents no number. See

1,0 0 0

1 0,0 0 0

1 0 0,0 0 0 1,000,000 10, 0 0 0,0,0.0 1 0 0, 0 0 0,0 0 0 2 0 0,0 0 0,0 0 2 3 0 0,0 0 3,0 3 0 4 0 4, 0 4 0,4 0 0 5 5 0, 5 0 0,0 0 0

1 thousand

10 thousand

100 thousand

1 million

10 millions - 100 millions

200 millions and 2

300 millions 3 thou. and 30 404 millions 40 thou. 4 hun. 550 millions 500 thousand EXAMPLES.

Read the following numbers, or write them in words. Note.-Making a point or dot after every third figure, counting from the units place, greatly facilitates the reading of large numbers.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 30, 31, 32, 40, 43, 44, 50, 55, 56, 60, 67, 68, 70, 71, 79, 80, 82, 83, 90, 92, 100, 101, 111, 112, 113, 114, 120, 128, 130, 132, 200, 203, 210, 300, 320, 332, 400, 500, 600, 700, 800, 900, 1000, 2001, 3010, 4020, 5200, 10250, 23450, 356789, 6789402, 76450791, 20156789, 1304136784.

Write the following numbers in figures:

Ten. Twelve. Fifteen. Seventeen. Twenty-six. Thirtynine. Fifty-two. Seventy-four. Eighty-one. Ninetysix. One hundred and fifteen. Two hundred. Three hundred and twenty. Nine hundred and nine. One thousand two hundred. Seven thousand seven hun