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. To write four thousand two hundred sixty-nine, we write 4 in the place of thousands, 2 in the place of hundreds, 6 in the place of tens, and 9 in the place of units. 29. The greatest number of the fourth order that can be expressed by four figures is 9999. EXAMPLES. 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. 10. One thousand nine hundred four. Read the following numbers: 11. 76; 128; 405; 910; 116; 3416; 1025. 12. 2100; 5047; 7009; 4670; 3997; 1001. 30. Next to thousands come tens of thousands, the fifth order, and next to these come hundreds of thousands, the sixth order, as tens and hundreds come in their order after units. Ten thousand is expressed by writing the unit 1 with four ciphers at its right. Thus, 10000. One hundred thousand is expressed by writing the unit 1 with five ciphers at its right. Thus, 100000. We can express thousands, tens of thousands, and hundreds of thousands in one number, in the same manner as we express units, tens, and hundreds in one number. To express five hundred twentyone thousand eight hundred three, we write 5 in the sixth place, counting from units, 2 in the fifth place, 1 in the fourth place, 8 in the third place, 0 in the second place (because there are no tens), and 3 in the place of units. Thus, 521803. 5 2 8 3 31. The greatest number of the fifth order that can be expressed by five figures is 99999; and of the sixth by six figures, 999999. EXAMPLES. 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. Two hundred twenty thousand. 11. One hundred fifty-six thousand. 12. Eight hundred forty thousand three hundred. 13. Five hundred one thousand nine hundred sixtyfour. 14. One hundred thousand one hundred. 15. Three hundred thirtee thousand three hundred thirteen. Read the following numbers: 16. 5006; 12304; 96071; 5470; 203410. 17. 36741; 400560; 13061; 49000; 100010. 18. 200200; 75620; 90402; 218094; 100101. For convenience in reading large numbers, point them off, by commas, into periods of three figures each, counting from the righthand or unit figure. This pointing enables us to read the hundreds, tens, and units in each period with facility. 32. Next above hundreds of thousands we have, successively, units, tens, and hundreds of millions, and then follow units, tens, and hundreds of each higher name, as seen in the following table: The number is read 530 quadrillion, 45 trillion, 370 billion, 36 million, 408 thousand 60. This is called the French method of pointing off the periods, and is the one in general use in this country. EXAMPLES. Write in figures, and read the following numbers: 1. One unit of the third order, four of the second. 2. Three units of the ffth order, two of the third, one of the first. 3. Eight units of the fourth order, five of the second. 4. Two units of the seventh order, nine of the sixth, four of the third, one of the second, seven of the first. 5. Three units of the sixth order, four of the second. 6. Nine units of the eighth order, six of the seventh, three of the fifth, seven of the fourth, five of the third, two of the second, nine of the first. 7. Four units of the tenth order, six of the eighth, four of the seventh, two of the sixth, one of the third, five of the second. 8. Eight units of the twelfth order, four of the eleventh, six of the tenth, nine of the seventh, three of the sixth, five of the fifth, three of the fourth, two of the third, seven of the second, eight of the first. 33. From the foregoing explanations and illustrations, the following important principles may be derived: 1. Figures have two values, Simple and Local. The Simple Value of a figure is its value when taken alone. Thus, 2, 5, 8. The Local Value of a figure is its value when used with another figure or figures in the same number. Thus, in 842 the simple values of the several figures are 8, 4, and 2; but the local value of the 8 is 800; of the 4 is 4 tens, or 40 ; and of the 2 is 2 units. 2. The local value of a figure depends upon its place from units of the first order, not upon the value of the figures at the right of it. Thus, in 425 and 400, the value of the 4 is the same in both numbers, being 4 units of the third order, or 4 hundred. Care should be taken not to mistake the local value of a figure for the value of the whole number. For, although the value of the 4 (hundreds) is the same in the two numbers, 425 and 400, the value of the whole of the first number is greater than that of the second. 3. A digit or figure, if used in the second place, expresses tens; in the third place, hundreds; in the fourth place, thousands; and so on. 4. Every period contains three figures (units, tens, and hundreds), except the last period to the left hand, which sometimes contains only one or two figures (units, or units and tens). 5. As ten units make 1 ten, 10 tens 1 hundred, 10 hundreds 1 thousand, and ten units of any order, or in any place, make 1 unit of the next higher order, or in the next place at the left, we readily see that the Arabic method of notation is based upon the following laws: Two GENERAL LAWS. I. The value of units of the different orders increases from right to left, and decreases from left to right, in a tenfold ratio. II. Every removal of a figure one place to the left, increases its local value tenfold; and every removal of a figure one place to the right, diminishes its local value tenfold. Thus, 6 is 6 units. 60 is 10 times 6 units. 600 is 10 times 6 tens. 6000 is 10 times 6 hundreds. 60000 is 10 times 6 thousands. |