Q. Now, as it takes 10 units to make one ten, or one in the next lefthand place, and 10 tens to make 100, how do figures appear to increase by being removed one place farther to the left? A. In a tenfold proportion, from right to left. You must have acquired, by this time, some considerable knowledge of figures: let me examine you a little; and, in the first place, let me see you write down on the slate the figure 4. Q. What do you call it ? A. 4 units. Write at the left of the 4, the figure 3, (thus, 34.) Q. What do you call them both, and how are they read? Write at the left of the 34 the figure 8, (thus, 834.) Q. What do you call the three figures now, and how are they read? A. 4 units, 3 tens, and 8 hundreds, read eight hundred and thirty-four. Write at the left of 834 the figure 1, (thus, 1834.) Q. What do you call the 4 figures now, and how read? A. 4 units, 3 tens, 8 hundreds, and 1 thousand, read one thousand eight hundred and thirty-four. Q. We have now been combining, or placing figures together, till we have obtained the number 1834, representing the number of years it is since Christ appeared on earth, to the present time. We might continue to put figures together in this way, that would express higher numbers still, up to billions, &c. That you may be able to form some idea of the power of figures, let me tell you that there not a billion of seconds in thirty thousand years; notwithstanding there are 60 seconds in every minute, 60 minutes in every hour, 24 hours in every day, and in a solar year, 365 days, 5 hours, 48 minutes, and about 48 seconds. Should we continue to go on as we began, in combining more figures still, it would be very inconvenient: to avoid this, we have a rule by which we can read almost any number of figures, ever so large. What is this rule called? A. Numeration. Q. What is the reading or expressing a number by figures, as now shown, called? A. Notation or Numeration. RULE. Q. From the above illustrations, how does it appear that you must begin to numerate? A. Begin at the right hand. Q. At which hand would you begin to read? A. The left. Q. What is the first figure at the right hand, or first place, caned? Q. What is the second figure, or second place, called ? A. Tens. Q. What is the third place called? A. Hundreds. Q. What is the fourth place called? A. Thousands. Q. In reading, what value do you give those figures which were called units in numerating? A. Units. Q. What value do you give tens? A. Tens. Q. What value do you give hundreds, thousands, &c.? Q. Will you repeat the Numeration Table, beginning with units, tens, &c.? Or, more commonly, thus, 1 Hundreds of millions. Hundreds of thousands. THOUSANDS. ∞ Hundreds. UNITS. 1, 2 3 4 5 6 7 8 9 1, ? Which, by putting their values together, are read thus: One billion, two hundred and thirty-four million, Are hundred and sixty-seven thousand, eight hundred and ninety-one. Questions on the Table. Q. What is the value of 9 with one cipher on the right of it? What the value of 8 with two ciphers? Of 7 with three ciphers? Of 6 with four ciphers? Of 5 with five ciphers? Of 4 with six ciphers? Of 3 with seven ciphers? Of 2 with eight ciphers? Of 1 with nine ciphers? Q. What is the meaning of annex? A. To place after. Q. What is the meaning of prefix? Let the scholar write down, in figures, the answers to the following questions on his slate at recitation. Q. How much does 1, with 1 cipher annexed, stand for? A. Ten. Q. Why? A. Because the 1 is tens, when I numerate. Q. What does 1 with 3 ciphers stand for? A. One thousand. Q. Why? A. Because, when I numerate, by saying 'Units, tens, hundreds, thousands,' the 1 comes thousands Q. What does 5 with five ciphers stand for? A. Five hundred thousand. Q. Why? A. Because, when I numerate, the 5 comes hundreds of thousands. Numerate and see. Q. What does 8 with 6 ciphers stand for? Q. Why? A. In numerating, the 8 comes millions. Numerate and see. Q. How do you read the figures 624 ? A. Six hundred and twenty-four. Q. What do the figures 6278 stand for? A. Six thousand two hundred and seventy-eight. Q. How do you know that the 6 is 6 thousand ? Q. How do you read the figures 56768? How do you read the figures 27365? How do you read the figures 654212? Express in words the following numbers. Note. The pupil may learn the value of each succeeding number by a former one. Express in figures the following numbers. Sixty. One hundred and twenty-five. Three million, three hundred thirty-three thousand, Oiree hundred and thirty-three. Thirty million. Three hundred million and twenty-five. Q. Will you repeat the following NUMERATION TABLE? Hundreds of quintillions.* Hundreds of quadrillions. Hundreds of trillions. c Hundreds of b.lions. Tens of billions. IIundreds of millions. Hundreds of thousands. cr BILLIONS. C MILLIONS. C THOUSANDS. Hundreds. 5 5 5,5 5 5, 55, 5 5,5 5 5,5 5 5, 5 5 5. Q. Will you now repeat the combined value of each figure 5 which is prefixed to the foregoing Table? A. Five hundred and fifty-five quintillion, five hundred and fifty-five quadrillion. five hundred and fifty-five trillion, five hundred and fifty-five billion, five hundred and fifty-five million, five hundred and fifty-five thousand, five hundred and fifty-five. SIMPLE ADDITION. ¶ VII. 1. You bought an orange for 9 cents, and a melon for 15 cents; what did you pay for both? 2. James bought a top for 6 cents, a knife for 12 cents, and an irkstand for 8 cents; how much did they all come to 3. Harry and James lost some money; James lost 20 cents, and Harry 12; how much did both lose? 4. A boy laid out 10 cents in marbles, 8 cents in quills, and 6 cents for a slate pencil; how much did he lay out in all ? 5. You give 40 cents for a Practical Arithmetic, 8 cents for a ruler, 9 cents for an inkstand, and lose 6 cents much money has gone from you? how 6. A mun gave his children money in the following manner; to his oldest 3 dollars, to James 5 dollars, to Thomas 9 dollars, and to his two daughters 4 dollars apiece; how much did he give away? * In like inunner we may go from quintillions to sextillions, septillions, octlkoms, nonillions, decillions, undecillions, duodecillions, &c. |