3. If a letter is placed before one of greater value, its value is to be taken from that of the greater. Thus, IX represents nine, XL forty, CD four hundred. 4. If a letter is placed between two letters, each of greater value, its value is to be taken from the sum of the other two. Thus, XIV represents fourteen, XXIX twenty-nine, XCIV ninety-four. 5. A bar or dash placed over a letter increases its value one thousand times. Thus, V signifies five, and V five thousand; L fifty, and L fifty thousand. The system of Roman Notation is not well adapted to the purposes of numerical calculation; it is principally confined to the numbering of chapters and sections of books, public documents, etc. Express the following numbers by letters: 1. Eleven. Ans. XI. 2. Fifteen. Ans. XV. 3. Twenty-five. Ans. XXV. 4. Thirty-nine. Ans. XXXIX. 5. Forty-eight. Ans. XLVIII. 6. Seventy-seven. Ans. LXXVII. 7. One hundred fifty-nine. 8. Five hundred ninety-four. 9. One thousand five hundred thirty-eight. 10. One thousand nine hundred ten. 11. Express the present year. 12. One thousand eight hundred ninety-three. 13. Thirty-four. 14. One hundred eighty-nine. 15. Three hundred seventy-eight. 16. Six hundred thirty-nine. 17. Express the year in which Columbus discovered America. 18. Express the year in which the Declaration of Independence was made. 19. Eighty-four. 20. Six thousand eight hundred ninety-seven, 21. Four hundred forty-four. 22. Nineteen. 23. Three thousand seven hundred forty-eight. 24. Eighty-eight. 25. One thousand one hundred fifty. 26. Five thousand seventy-three. 27. Ten thousand five hundred. 28. One million ten thousand. 29. One million one hundred ten thousand. 30. One hundred thousand two hundred. 31. Five hundred thousand six hundred forty-three. THE ARABIC NOTATION. 17. The Arabic Notation employs ten characters or figures to express numbers. FIGURES. 0 1 2 2 3 4 5 6 7 8 9 NAMES. Naught. One. Two. Three. Four. Five. Six. Soven. Eight. Nine. 18. The first character is called naught, or cipher, because it has no value of its own. It is also called nothing and zero. 19. The other nine characters are called significant figures, because each has a value of its own. The significant figures are also called digits, a word derived from the Latin term digitus, which signifies finger. 20. These ten characters are the alphabet of arithmetic, and by combining them according to certain principles, all numbers can be expressed. 21. These ten characters, when standing singly, constitute the first order, or order of units. 22. Each of the nine digits has a value of its own; hence any number not greater than nine can be expressed by one figure. 23. As the Arabic Notation is a decimal notation* based on the number ten (decem), the number ten begins a second order. This is called the order of tens. One ten is expressed by writing the unit 1 with the cipher, 0, at its right, 10; 1 is in the order of tens and 0 in the order of units. * For other schemes of notation, see pp. 156–159. We express the numbers between 10 and 20 by writing the 1 with each of the digits respectively at its right; thus Eleven. Twelve. Thirteen. Fourteen. Fifteen. Sixteen. Seventeen. Eighteen. Nineteen. 11 12 13 14 15 16 17 18 19 In like manner we express the numbers between 20 and 30, between 30 and 40, and between any two successive tens. Thus, 21, 22, 23, 24, 25, 26, 27, 28, 29, 34, 47, 56, 68, 72, 89, 93. 24. The greatest number of the second order that can be expressed by two figures is 99. 25. The number one hundred begins the third order. This is called the order of hundreds. One hundred is expressed by writing the unit 1 with two ciphers at its right. Thus, 100. In the same manner we represent One Two Three Four Five Six Seven Eight Nine hundred. hundred. hundred. hundred. hundred. hundred. hundred. hundred. hundred. 100 200 300 400 500 600 700 800 900 We express the numbers between 100 and 999 by writing the figure of the hundreds' order with the proper figures of the tens' and units' orders at its right, remembering that when there are no tens or units to be represented, a cipher must be put in their place. Thus, 101, 109, 120, 156. 26. The greatest number of the third order that can be expressed by three figures is 999. 27. PRINCIPLES. - 1. When a number is expressed by one figure, it represents units. 2. When a number is expressed by two figures, the righthand figure represents units and the left-hand figure tens. 3. When a number is expressed by three figures, the righthand figure represents units, the next figure tens, and the left-hand figure hundreds. EXAMPLES. 1. Write one hundred twenty-five. 28. The number one thousand begins the fourth order. This is called the order of thousands. One thousand is expressed by writing the unit 1 with three ciphers at its right. Thus, 1000. In the same manner we represent One thousand. Two thousand. Three thousand. Four thousand. Floa thousand 1000 2000 3000 4000 500 Six thousand. Seven thousand. Eight thousand. Nine thousand |