Laws of Notation and Numeration. 3. 1. A figure standing alone, or at the right of one or more figures, expresses the number of Units or single things. 2. A figure in the second place from the right expresses the number of Tens or groups of ten single things. 3. A figure in the third place from the right expresses the number of Hundreds or groups of ten tens. 4. The cipher is used to locate significant figures in their proper positions. 4. Express in figures the following: 1. Eight; five; seven; four; nine; nine and one. 2. Three tens; nine tens; six tens; two tens; 8 tens; nine tens and one ten. 3. Six hundred; four hundred; 3 hundred; 9 hundred. 4. Ten and three; ten and nine; ten and seven; 2 tens and three; 5 tens and 2. 5. Nine tens and seven; 8 tens and 4; 6 tens and 9; 3 tens and 7; 9 tens and 7. 6. Five tens and nine; 9 tens and 3; 4 tens and 8; 7 tens and 3; 9 tens and 9. 7. Nine tens and one; one hundred two tens; one hundred nine; four hundred seven. 8. Two hundred seven tens and two; 5 hundred 9 tens and 1; 8 hundred 3. 9. Seven hundred 4; 9 hundred 6; 4 hundred eight tens. 10. 4 hundred ten; 8 hundred one; 3 hundred 2. 11. 9 hundred 9 tens; 9 hundred 9; 9 hundred 9 tens and 9. 12. How many tens, and how many units are 39? 13. How many hundreds, and how many tens are 750? 14. How many hundreds, and how many units are 408? 15. How many hundreds, tens, and units are 396? 5. PROP. II.-The names of numbers are formed by combining the names of the figures used to express the numbers with the names of the orders of groups represented. 1. 11 is ten and one, read Eleven. 12 is ten and two, read Twelve. These two numbers are the only exceptions to the proposition. 2. The names of numbers from twelve to two tens are formed by changing ten into teen, and prefixing the name of the digit which expresses how many the number is greater than ten. The name of the digit, when necessary to combine properly with teen, is changed, thus: 13 is three and ten, or Thir-teen; three changed to thir. 14 is four and ten, or Four-teen. 15 is five and ten, or Fif-teen; five changed to fif. 16 is six and ten, or Six-teen. 17 is seven and ten, or Seven-teen. 18 is eight and ten, or Eigh-teen; eight changed to eigh. 19 is nine and ten, or Nine-teen. 3. The name of any number of tens from one ten to ten tens is formed by changing the word tens to ty and prefixing the name of the digit which expresses the required number of tens, making the necessary changes in the name of the digits to combine properly with ty, thus: 20 is two tens, or Twen-ty; two changed to twen. 70 is seven tens, or Seven-ty. 80 is eight tens, or Eigh-ty; eight is changed to eigh. 90 is nine tens, or Nine-ty. 4. Tens, and ones or units, when written together, are read by uniting the two names in one, thus: 21 is two tens and one, read Twenty-one. 35 is three tens and five, read Thirty-five. 5. Hundreds are read by naming the digit that expresses them. Thus, 400 is read Four hundred. 6. Hundreds, tens, and units, when written together, are read by uniting the three names. Thus, 683 is read Six hundred eighty-three. 6. Read the following numbers: 1. 17. 13. 19. 12. 18. 14. 11. 15. 10. 16. 2. 30. 70. 40. 80. 60. 90. 24. 54. 84. 93. 99. 3. 500. 200. 700. 410. 820. 390. 605. 903. 509. 936. 473. 897. 369. 704. 990. 4. 783. 625. 5. 888. 111. 273. 909. 990. 999. 777. 222. Name the orders in the following numbers commencing at the right. Thus, 839 is 9 units, 3 tens, and 8 hundreds. 6. 493. 765. 892. 375. 906. 580. 734. 983. 306. 7.572. 409. 603. 942. 300. 850. 903. 872. Read and analyze the following, thus: 8. 37 horses. ANALYSIS.-Thirty-seven horses may be regarded as 3 groups of ten horses and 7 single horses, or as 37 single horses. 9. 542 trees. ANALYSIS.-Five hundred forty-two trees may be regarded as 5 groups of one hundred trees each, 4 groups of ten trees each, and 2 single trees; or it may be regarded as 54 groups of ten trees each aud 2 single trees; or as 542 single trees. 10. 67 tops. 46 rings. 14 boys. 17 men. 11. 127 tables. 108 beds. 12. 696 beetles. 13. 444 robins. 14. 196 lambs. 15. 303. 940. 75 sheep. 205 chairs. 511 stoves. READING LARGE NUMBERS. 7. PROP. III.—The names of the orders in large numbers are formed by giving a new name to the order in every third place counting FROM the UNITS. 1. We indicate the orders to which new names are applied by inserting a comma at the left of every third figure, counting from the right. The commas are inserted and the names applied; thus, 73,069,294,78 0,569 5th Period. 4th Period. 3d Period. 2d Period. 1st Period. 2. The commas separate the number into sets of three figures. Each set is called a Period. 3. The right-hand order in each period has a new name, as shown in the illustration. The figure in this place expresses ones of the given name. 4. The second figure in each period expresses tens, and the third hundreds, of whatever the first order is called. For example, the figures in the third period of the above number are 294, and the right-hand order is called millions; hence the period is read, two hundred ninty-four millions. 5. The figures in each period are read in the same manner as they would be if there were but one period in the number. Thus, in the above number, the fifth period is read, seventythree trillions, the fourth is read, sixty-nine billions. There being no hundreds expressed in the fourth period nothing is said about hundreds. Each succeeding period is read in the same manner. 6. A large number can be read as easily as a number of three places, when the following names of the first order on the right of the successive periods are fixed in the memory: From these illustrations, we obtain for reading numbers the following RULE.-I. Begin at the right and separate the number, by inserting commas, into periods of three figures each. II. Begin at the left and read the hundreds, tens, and ones of each period, giving the name of the ones in each case except in the last period. EXAMPLES FOR PRACTICE. 8. Point off and read the following numbers: 1. 307. 560. 293. 1348. 4592. 8347. 6241. 6. 8060. 50040. 3040006. 2406007. 5030062. 7. 9000000. 40006003. 60304090. 200006000. 300000804. 8. 800800800800. 3005006004. 407000060060. 9. 806042. 35064. 9003005. 100100100101. 10. 3000050030. 8300400706005. 9000100130004. |