ARITHMETIC BOOK TWO CHAPTER I Arithmetic is the science of numbers and includes the art of computation. The fundamental operation in arithmetic is counting. A unit is one thing, or a group of things regarded as a single thing. Each number has a name, as one, ten, one hundred. Numbers may be written in words, or by the use of symbols, as 5, XIX. The symbols in general use among us are called figures, as 5, 6. These figures are arranged in a regular plan or system, easy to read. This system is commonly called the Arabic System. Writing numbers according to a system is called Notation. Reading numbers so written is called Numeration. NOTATION Every number can be expressed by one or more of the following figures, sometimes called Arabic Numerals: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. The first nine of these are called digits, or significant figures, and the tenth is called zero, or cipher. In writing a number zero is used to fill a place not named as occupied by some other figure; thus, Forty million, five hundred six thousand, twenty-three is written: 40,506,023. To represent numbers above nine, two or more figures are written side by side. Thus, twenty-nine is written 29; four hundred fifty-three is written 453. Notice in 29 that "9" represents "nine," and that the "2" at the left of the "9" represents "twenty; " also, in four hundred fifty-three, the "3" represents "three," the "5" represents "fifty," and the "4" represents "four hundred." The right-hand figure stands for ones, the next figure to the left stands for tens, the next to the left, hundreds, and other figures stand for different values according to the positions they occupy. These positions are sometimes called orders. In numbers expressed by more than three figures, it is customary to use commas to separate the number into groups of three figures, beginning at the right. The left-hand group may contain less than three figures; thus, 79,409,700. It is to be noticed that the figure 0 has no value in any position, except to fill it, and that the value of a significant figure depends upon the figure and the place. The following table gives the names and positions of the units up to units of the fifteenth order. It also gives the first five periods. The period at the right is called the units' period; the next, the thousands' periods; the next, the millions' period; and so on. Write in figures: EXERCISE 1 1. Four thousand, eight hundred twenty-seven. 2. Nine thousand, seven hundred one. 3. Sixty-eight thousand, four hundred fifty-two. 6. Eighty-seven thousand, one hundred one. 9. Eighteen thousand, eighteen. 13. Fifty-four thousand, eleven. 14. Seventy-three thousand, one. 15. Six hundred four thousand, two hundred one. 16. One hundred sixty-three thousand, ten. 17. One hundred one thousand, three hundred. 18. One hundred thousand, seven. 19. Four hundred ten thousand, one hundred twenty seven. 20. Five hundred four thousand, three hundred eight. 21. Five hundred thousand, eleven. 22. Six hundred thousand, seventeen. 23. Nine hundred ninety thousand, fifteen. |