ARITHMETIC.

CHAPTER I.

NUMBERS.

1. A FUNDAMENTAL IDEA, like that of number, cannot be defined. A number is the simple, direct answer to the question, How many?

2. A system of naming numbers is called numeration, and a system of representing numbers by symbols is called notation.

The first twelve numbers, formed by adding one thing at a time, are named:

One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.

These numbers are represented by Arabic figures, or digits, as follows:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

3. The digit 0, called naught, zero, or cipher, is used as a symbol of the words "none" or "nothing." A digit written in the second place to the left of another digit signifies tens. Thus, 10 is one ten and nothing; 11 is one ten and one; 12 is one ten and two; 23 is two tens and three; etc., etc.

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4. The next seven numbers, 13, 14, 15, 16, 17, 18, 19, are the teens: thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen.

5. Two tens are called twenty; three tens, thirty; four, forty; five, fifty; six, sixty; seven, seventy; eight, eighty; nine, ninety.

etc.

Thus, 57 is fifty-seven; 63, sixty-three; 89, eighty-nine;

6. Read the numbers:

14, 13, 11, 12, 19, 18, 17, 16, 15, 10, 20, 22, 21, 27, 26, 25, 28, 23, 24;

30, 32, 31, 36, 38, 34, 35, 37, 33, 29, 44, 55, 66, 77, 43, 52, 61, 42, 41, 45, 49, 57, 47, 60, 56;

67, 76, 53, 39, 58, 75, 77, 83, 87, 92, 91, 96, 87, 99, 98, 85, 74, 84, 48, 46, 44, 64, 65, 63.

7. Ten tens are one hundred; and hundreds are written in the third place toward the left; thus:

100, one hundred; 700, seven hundred; 823, eight hundred twenty-three; 941, nine hundred forty-one; 607, six hundred seven.

8. Read the numbers:

121, 222, 78, 780, 778, 708, 827, 741, 531, 712, 231, 365, 474, 439, 143;

534, 587, 932, 239, 392, 617, 761, 176, 873, 246, 789, 879, 987, 978, 934, 543, 897;

707, 680, 704, 518, 405, 903, 319, 309, 104, 870, 801, 807, 708, 610, 909, 120, 201.

9. Write in figures:

Seventeen, seventy, nineteen, ninety-three, sixteen, sixtyseven, fourteen, forty-five, fifty-nine;

One hundred three, seven hundred nineteen, three hundred three, six hundred eight, six hundred eighteen, six hundred eighty;

Nine hundred ten, five hundred six, eight hundred eightyeight, four hundred twenty-seven, seven hundred sixtyfive, two hundred eleven.

10. Ten hundred make one thousand, and thousands are written in the fourth place to the left.

Tens of thousands are written in the fifth place, hundreds of thousands in the sixth place.

A comma is usually placed among the figures at the point where, in reading, the word thousand comes.

Thus, 621,453 is 621 thousand, 453; and 700,006 is 7 hundred thousand, six.

11. Read the numbers:

1000; 7000; 7842; 1067; 5043; 8375; 18,757; 75,764; 234,567; 34,561; 123,456;

654,089; 600,897; 607,804; 2753; 704,608; 900,008; 806,042; 709,053; 350,709; 240,682; 118; 537; 3094; 5000; 50,000; 500,005; 682,000; 246,001; 753,110; 703,101; 930; 2020; 200,200; 708,056; 70,856; 870,890.

12. Write in figures:

Eight hundred thousand eight hundred eight; six hundred thousand six; seven hundred thirteen thousand three hundred nine.

Five hundred seventeen thousand six hundred thirteen; seven thousand eight hundred fifty-four; seven hundred eighteen thousand eight hundred eighty-nine.

13. A thousand thousands make a million; and millions up to 999 millions are written in the seventh, eighth, and ninth places.

Thus, 728,651,423 is 728 million, 651 thousand, 423.

14. Read the numbers:

21,978,564; 17,756,423; 300,200,100; 707,303,202;

312,406,780; 908,765,487; 2,632,561.

15. Digits are thus divided by commas into periods of three places each. Each period contains its own units' place, tens' place, and hundreds' place; but the unit in the first period, on the right, is one; in the second period, a thousand; in the third period, a million; and so on.

The first period is called the units' period; the second is the thousands' period; the third is the millions' period. A fourth period is the billions' period; a billion being a thousand millions; and the fifth period the trillions' period. The next periods, taken in order, are quadrillions, quintillions, sextillions, septillions, octillions, and so on.

16. We may read the number 1736 either as 1 thousand 736, or as 17 hundred 36. In like manner, we may read a larger number in a still greater variety of ways; thus, 2,736,000,000, may be read, 2 billions, 736 millions; or, 2 thousand 736 millions; or, 27 hundred 36 millions. To put this into the form of a rule :

When numbers are expressed in words, the name of a smaller number following a larger signifies that the two