Write one unit of the second order, (or one ten,) and one unit of the first order, (or one unit.) Ans. 11. Write one unit of the third order, (or one hundred,) and one ten, and one unit. Ans. 111. Write one hundred, one ten, and five units. Ans. 115. Ans. 237. Ans. 358. Two hundreds, eight tens, and nine units. Seven hundreds, six tens, and three units. Two tens, and two units. Nine tens, and six units. Four hundreds, and six tens, and four units. Five hundreds, five tens, and five units. Nine hundreds, seven tens, and three units. Four hundreds, eight tens, and four units. Eight hundreds, and nine tens, and nine units. Two hundreds, six tens, and three units. One hundreds, two tens, and three units. Two hundreds, five tens, and seven units. One ten, and three units, Seven tens, and three units. Nine hundreds, nine tens, and nine units. In all these examples, units of the first order, come first on the right; those of the second come second; those of the third come third; so that if the same kind of figures were used for all, we should know the several orders, by their places. Where do units of the first order come? Where do units of the second order come? Where do those of the third order come? Then, THE NUMBER OR NAME OF ANY ORDER, IS THE SAME WITH THE NUMBER OR NAME OF ITS PLACE, COUNTING FROM THE RIGHT. Ans. If we used the same figures for all the orders, how would you know the order to which any figure belonged? Then, using the common figures, write the following numbers. One ten, and one unit, or eleven. One ten, and two units, or twelve. One ten, and three units, or thirteen. Fourteen, or one ten, and four units. Fifteen, or one ten, and five units. Sixteen, or one ten, and six units. Seventeen, or one ten, and seven units. Eighteen, or one ten, and eight units. Nineteen, or one ten, and nine units. 11. 12. 13. 14. 15. 16. 17. 18. 19. One hundred and thirty-four, or one hundred, and three tens, and four units. Ans. 134. Seven hundred and sixty-three, or seven hundreds, and six tens, and three units. Now write one ten, or one ten and no units. Ans. 10, Here we see the use of the 0, or cypher; for if we were to write nothing but 1, it would read one unit of the first order, or one unit simply; because it would be in the first place. Now the cypher has no value, but it makes the 1 stand in the second place, and, therefore, makes it a unit of the second order, which is equal to ten units of the first. How do you write one ten? Why do you use the cypher? Why do you not use more cyphers than one? Has the cypher any value ? Does the use of it affect the value of other figures? Write two tens, or twenty. 20. Three tens, or thirty. 30. Four tens, or forty. 40. Five tens, or fifty. 50. Sixty, or six tens. 60. 100 Ten tens, are ten units of the second order, which are equal to one of the third order, or one hundred, written Why do you use two cyphers here? If I were to annex another cypher to 100, (as 1000,) in what place would the 1 stand? Ans. The fourth place. It would, then, be a unit of what order? fourth order. Ans. The A UNIT OF THE FOURTH ORDER IS CALLED A THOUSAND, If a cypher were annexed to 1000, (as 10000) to what order would the 1 belong? UNITS OF THE FIFTH ORDER ARE CALLED TENS OF THOUSANDS. Another cypher would make the 1, a uuit of what order? UNITS OF THE SEVENTH ORDER ARE CALLED MILLIONS, Read the following numbers. 5 Five, or five units. 30 Thirty, or three tens. 35 Thirty-five. 400 79 63 81 97 83 76 49 87 95 Four hundreds. 435 Four hundred and thirty-five. 553 984 659 334 695 843 7000 Seven thousands. 7435 Seven thousand, four hundred, and thirty-five. 80000 Eighty thousand or eight tens of thousands. 500000 Five hundred thousand, or five hundreds of thousands. 679458 234567 320320 427427 2000000 Two millions. 2587435 Two million, five hundred and eighty-seven thousand, four hundred and thirty-five. 2305061 8910002 8395421 7878978 2004 17 40002 10203 1000001 2222222 813 617 23904 237801 603545 7897989 6304026 [The teacher should require the pupil to read these numbers, both by the familiar names, and also, by the names of the orders; as 6 tens of thousands, instead of 60 thousand, &c. So, likewise, in writing the following numbers, the pupil should change the common names into the same terms.] Write the following numbers in figures. Three 3 30 Thirty, or three tens Thirty-three, or three tens, and three units. Forty-seven. Eighty-eight. Fifty-six. Thirty-five. Eight hundred 800 Eight hundred and thirty-three. Six hundred and ninety-eight. Five hundred and fifty-five. Eight hundred and fifteen. Two thousand 2000 Two thousand, eight hundred, and thirty-three. Four thousand, nine hundred, and eighty-one. Sixty thousand, or six tens of thousands, 60000 Sixty thousand, eight hundred, and thirty-three. Five hundred thousand, or five hundreds of thousands, 500000 Five hundred and sixty-two thousand, eight hundred, and thirty three. One million 1000000 One million, five hundred and sixty-two thousand, eight hundred, and thirty-three. Two hundred and three. Two thousand and three. Three million, eighty-five thousand, and twenty-one. Six hundred and fifty eight thousand, nine hundred and seventy eight. Three hundred and sixty-five, Nine Million three hundred and thirty-seven thousand, five hundred and fifty-four. Four hundred and eighty-eight thousand six hundred and seventy five. Forty-four thousand, eight hundred and ninety-nine. Five hundred and fifty-three. Seven hundred and ninety-one. IV. How many orders of figures have you learned? What is the seventh? The sixth? Fifth? Fourth? Third? Second? First? The other orders, as high as the 24th, may be learned from the following In order to read large numbers, it is very convenient to divide them into periods of three figures each, begining at the right. The first is called the periods of units, because it contains units, and tens of units, and hundreds of units. The second, the period of thousands, because it contains thousands, and tens of thousands, and hundreds of thousands, and so on. The names of the periods are given above. IN READING, YOU SHOULD READ EACH PERIOD AS THOUGH IT STOOD ALONE, AND THEN ANNEX THE NAME OF THE PERIOD. Thus, to read the period of thousands above, first read it as though it stood alone, and it will be, five hundred and fifty-five. Then annex the name of the period, and it will be, five hundred and fifty-five thousand. Let the pupil point off and read the following numbers. 7-8 6 4 3 7 9 2.5 8 4,2 19 5 1 1 1 1 9 9 9 9 3 8 7 6 5 3 1 2 3 4 5 6 7 8 9 0 0 0 0 0 24 7 6 0 0 0 0 7 6 0 0 0 0 76 9 1 8 7 5 6 7 8 1 2 3 5 4 1 0 0 1 8 0 9 0 1 0 3 0 4 0 0 0 2 3 4 5 7 8 9 0 0 0 6 7 8 0 0 5 6 7 0 2 3 4 2 3 1 2 5 6 1 6 5 8 7 1 2 4 8 9 6 7 4 5 0 0 0 2 0 3 0 1 0 2 1 0 7808 It is likewise most convenient to write numbers by periods. Write three hundred and five thousand, four hundred and fifty-three. How many periods are here mentioned, and what are they? Write the period of thousands. Ans. 305 thousands. Write the period of units. Which ought to stand first? Ans. 453. Then write them both together. Ans. 305,453. Write three hundred and five million, four hundred and fifty three. Write first the millions' period. There are no thousands; how will you write the thousand period? Ans. 000 thousands. Write the units period. Ans. 453. Arrange the periods in order. Ans. 305,000,453. Write sixteen thousand and thirty. Then, to write numbers in figures, BEGIN WITH THE HIGHEST PERIOD AND WRITE EACH PERIOD AS THOUGH IT WAS THE ONLY ONE TO BE WRITTEN. PLACE CYPHERS WHEREVER A PERIOD OR AN ORDER IS OMITTED. In this manner let the pupil write the following numbers. Write seven millions, six hundred and sixty-two thousand, five hundred and ninety-three. Four billions, twenty million, two hundred thousand and five. Four hundred and seventy-nine quadrillions, twenty-three million and sixty. One thousand and three. One hundred thousand, five hundred and forty. Seventy-seven million, four hundred and forty-two thousand, five hundred and nineteen. Sixty five trillions, seventy four billions, eighty four millions, ninety four thousand, one hundred and five. Two quadrillions and fifty. Nine quintillions and thirty nine. Seven sextillions, eighty five millions, three hundred and four. Five sextillions, three hundred and seventy nine quintillions, four hundred and forty seven quadrillions, eight hundred and twenty three trillions, four hundred and thirty seven billions nine hundred and eighty six millions five hundred and thirty six thousand four hundred and seventy nine. Two sextillions and two. V. Where the figure 1 stands alone, what is its value? Ans. One unit. When the figure 2 stands alone, what is its value? Ans. Two units. When 3 stands alone what is its value? When 4? 5? 6? 7? 8? 9? |