THE ARABIC NOTATION. 13 4. Six hundred and forty thousand, one hundred and one. 5. Nine million, fifty-seven thousand, and eight. 6. Eleven billion, forty-one million, two hundred and ten. 7. Thirty-six million, one hundred thousand, and twelve. 8. Ten billion, ten million, ten thousand, and three. 9. Six hundred and one million, two hundred thousand. 10. Eighty-nine thousand, three hundred and nineteen. 11. Twelve thousand, five hundred and eighty-seven. 12. Four hundred billion, four million, forty thousand. 13. Five million, eight hundred thousand, and seventy-five. 14. One billion, ten million, two hundred thousand, and six. 15. Fifty-seven million, three hundred and twenty-four. 16. Four million, two hundred, and seventeen thousand, and fifty-eight. 17. Six hundred and nine billion, four hundred and sixtysix million, ninety-two thousand, three hundred and twentyeight. The Roman Notation. 26. The Roman Notation is so called because it was used by the ancient Romans. It employs seven letters. I. denotes one; V., five; X., ten; L., fifty; C., one hundred; D., five hundred; M., one thousand. 27. These letters are combined to express numbers, according to the following principles: 1. If a letter is repeated, its value is repeated. XX. is twenty; III. is three. 2. A letter of less value, placed after one of greater, unites its value to that of the latter. VI. is six. 26. Why is the Roman Notation so called? What does it use, to express numbers ?--27. State the principles of the Roman Notation. 3. A letter of less value, placed before one of greater, takes its value from that of the latter. IV. is four. 4. A letter of less value, placed between two of greater, takes its value from that of the other two united. LIV. is fifty-four. 5. A bar over a letter increases its value a thousand times. V. is five thousand. TABLE. I. is One. V. "Five. VI." Six. VII. "Seven. VIII. "Eight. IX. "Nine. X. "Ten. XI. "Eleven. 眼 XII. "Twelve. XIII. Thirteen. XIV. XL. "Forty. C." One hundred. CI." One hund. and one. CX." One hund. and ten. D. "Five hundred. M. "One thousand. V. "Five thousand. What is the effect of placing a bar over a letter? How is five thousand denoted? Learn the Table. EXERCISE IN NOTATION. 15 28. We may, then, express numbers in three ways: 1. With words, as is usual in printed books. 2. With figures, by the Arabic Notation, as in accounts and calculations. 3. With letters, by the Roman Notation, as in the headings of chapters. EXERCISE IN NOTATION. Write the following numbers first by the Arabic, and then by the Roman, Notation: 1. Twelve. 2. Fifty-seven. 3. Nine hundred. 4. Eighty-six. 5. Nineteen. 6. One thousand. 7. Ninety-nine. 8. Seven hundred. 9. Sixty-two. 10. Four thousand. 11. Five thousand six hundred and seventy-three. 12. Three hundred and seventy-two. 13. Two thousand eight hundred and forty-one. 15. Fifteen hundred and thirty-five. Express the following numbers according to the Roman Notation: 12; 1,000; 749; 18; 203; 96; 660; 438; 29; 2,040; 85; 555; 10,801; 79; 5,002; 37; 394; 999; 2,062; 3,186; 119. Express the following numbers according to the Arabic Notation: XII. LI. VIII. XLIII. XVI. LXXXIX. XCVIII. CCI. DXX. XXXIV. MD. IX. MCCXV. DCCCVII. XIV. MDCLXVI. V. x. vii. lv. cciv. xxxiii. xix. xlviii. xc. cxxi. xv. lxii. 28. How many ways are there of expressing numbers? What are they, and where is each used? NUMERATION. 29. Numeration is the art of reading numbers expressed by figures. 30. In reading numbers, the following principles apply: 1. We read by periods. Hence, if there are more than three figures, point off the number into periods of three figures each, beginning at the right. 2. Always begin to read at the left. 3. The right-hand figure and the right-hand period are never named as units, the word units being understood. We read 7 as seven, not seven units; 400 is read four hundred, not four hundred units. 4. Places containing 0 must be passed over in reading. We read 1062 one thousand and sixtytwo, not one thousand, no hundred, and sixty-two. 31. RULE.-Beginning at the right, point off the number into periods of three figures each. Beginning at the left, read the figures in each period as if they stood alone, adding the name of the period in every case except the last. EXAMPLES. 10,709 Ten thousand, seven hundred and nine. 401,840 Four hundred and one thousand, eight hundred and forty. 6,023,070 Six million, twenty-three thousand, and seventy. 29. What is Numeration ?-30. How do we read numbers? If there are more than three figures, what do we do? At which side do we begin to read? What is said of the right-hand figure and the right-hand period? What must be done in the case of places containing 0?-31. Give the rule for Numeration. EXERCISE IN NUMERATION. 17 42,110,000 Forty-two million, one hundred and ten thousand. 870,025,002 Eight hundred and seventy million, twenty-five thousand, and two. 1,001,000,011 One billion, one million, and eleven. 19,056,007,000 Nineteen billion, fifty-six million, seven thousand. 123,400,789,000 One hundred and twenty-three billion, four hundred million, seven hundred and eighty-nine thousand. 1100 is read one thousand one hundred, or eleven hundred. one thousand two hundred, or twelve hundred, &c. 1200" EXERCISE IN NUMERATION. Read the following numbers: REVIEW QUESTIONS.-What is a Unit? What is a Number? Of what does Arithmetic treat? What is Counting? What is Notation ? Name the two systems of notation. What characters are used in the Arabic Notation? Name the periods in order, beginning at the right. Name the places. Give the rule for expressing numbers in figures. What characters are used in the Roman Notation? State the princi ples on which they are combined. What are used to express numbers, in making calculations? What, in accounts? What, in headings of chapters? What is Numeration? Give the rule for reading numbers. |