4. When 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. THE ARABIC NOTATION.* 19. This system of notation employs ten characters or figures to express numbers. FIGURES. O 1 2 3 4 5 6 7 8 9 Six Seven Eight Nine 20. The first character is called naught, cipher, or zero, because it has no value of its own. The other nine characters are called significant figures, because each has a value of its own. * A fuller presentation of the numbers from 1 to 100 will be found in the Introductory Exercises. 21. As we have no single character to represent ten, we express it by writing the unit, 1, at the left of the cipher, 0. Thus, 10. 22. When a number is expressed by two figures, the right hand figure is called units, and the left hand figure tens. The greatest number that can be expressed by two figures is 99. 23. We express one hundred by writing the unit, 1, at the left hand of two ciphers. Thus, 100. In like manner we write two hundred, 200, three hundred, 300, etc., to nine hundred, 900. 24. When a number is expressed by three figures, the right hand figure is called units, the second figure tens, and the left hand figure hundreds. The greatest number that can be expressed by three figures is 999. Express the following numbers by figures: 1. One hundred twenty. 4. Nine hundred. 5. Two hundred ninety. 6. Eight hundred nine. 25. We express one thousand by writing the unit, 1, at the left hand of three ciphers. Thus, 1000. In the same manner we write two thousand, three thousand, etc., to nine thousand; thus, 26. When a number is expressed by four figures, the places, commencing at the right hand, are units, tens, hundreds, thousands. To express hundreds, tens, and units with thousands, we write in each place the figure indicating the number we wish to express in that place. Thus, to write four thousand two hundred and sixty-nine, we write 4 in the place of thousands, 2 in the place of hundreds, 6 in the place of tens, 9 in the place of units; thus, The greatest number that can be expressed by four figures is 9999. Express the following numbers by figures: 1. One thousand two hundred. 2. Five thousand one hundred sixty. 3. Three thousand seven hundred forty-one. 4. Eight thousand fifty-six. 5. Two thousand ninety. 6. Seven thousand nine. 7. One thousand one. 8. Nine thousand four hundred twenty-seven. 9. Four thousand thirty-five. 10. One thousand nine hundred four. Read the following numbers: 11. 76 128 405 910 116 3414 1025. 12. 2100 5047 7009 4670 3997 1001 5639. 27. Next to thousands come tens of thousands, and next to these come hundreds of thousands, as tens and hundreds come in their order after units. Write the following numbers in figures: 1. Twenty thousand. 2. Forty-seven thousand. 3. Eighteen thousand, one hundred. 4. Twelve thousand, three hundred fifty. 5. Thirty-nine thousand, five hundred twenty-two. 6. Fifteen thousand, two hundred six. 7. Eleven thousand, twenty-four. 8. Forty thousand ten. 9. Sixty thousand, six hundred. 10. Eight hundred forty thousand, three hundred. Read the following numbers: 11. 5006 12. 36741 12304 96071 5470 203410. 400560 13061 49000 100010. For convenience in reading large numbers, we may point them off, by commas, into periods of three figures each, counting from the right hand or unit figure. This pointing enables us to read the hundreds, tens, and units in each period with facility as seen in the following table: 28. Figures occupying different places in a number, as units, tens, hundreds, etc., are said to express different orders of units. 29. In numerating, or expressing numbers verbally, the various orders of units have the following names: Write and read the following numbers: 1. One unit of the third order, two of the second, five of the first. Ans. 125; read, one hundred twenty-five. 2. Two units of the 5th order, four of the 4th, five of the 2d, 6 of the 1st. Ans. 24056; read, twenty-four thousand fifty-six. 3. Seven units of the 4th order, five of the 3d, three of the 2d, eight of the 1st. 4. Two units of the 6th order, nine of the 5th, four of the 3d, one of the 1st, seven of the 2d. 5. Three units of the 6th order, four of the 2d. 6. Nine units of the 5th order, seven of the 4th, nine of the 1st. 7. Four units of the 7th order, two of the 6th, one of the 3d, five of the 2d. 8. Eight units of the 7th order, three of the 6th, five of the 5th, two of the 3d, eight of the 1st. |