UNITS, TENS, HUNDREDS. 11. Ten, we have seen, is expressed thus-10. Then 1 in the second place denotes one ten. So, 2 in the second place (20) is two tens, &c. Any figure standing in the second place represents so many tens. Hence it denotes ten times as much as if it stood in the first place. 12. The first place is called the units' place. The second is the tens' place. 13. Numbers greater than 99 must be expressed with more than two figures. A third place is thus required, which is called the hundreds' place. A figure in the third place denotes ten times as much as if it stood in the second place, and a hundred times as much as if it stood in the first place. 14. To express the even hundreds, place the several figures in the third place, with naughts after them. Thus: 100 one hundred 200 two hundred 300 three hundred 400 four hundred, &c. 15. Observe how the numbers between the even hundreds are expressed : 11. How is ten expressed? What does 1 in the second piace denote? 2 in the second place? Any figure in the second place ?-12. What is the first place called? What is the second place called?-13. How must numbers greater than 99 be expressed? What is the third place called? What value is denoted by a figure in the third place, compared with the second and the first?-14. How are the even hundreds expressed?-15. Learn how to express numbers between the even hundreds. THE ARABIC NOTATION. 9 EXERCISE. Count from 300 to 400. Count backwards from 900 to 800. Write on your slate the numbers from 500 to 600. Write 3 units, 6 tens, 9 hundreds (963); 9 units, 6 tens, 3 hundreds; 7 tens, 5 units; 8 hundreds; 3 hundreds, 6 units; five hundreds, one ten; two tens. Express in figures three hundred and ninety-six. Two hundred and twelve. Eighty-one. Four hundred and two. Eight hundred and thirty. Six hundred. Seventeen. THOUSANDS. 16. The greatest number that can be expressed with three figures, is 999. Next comes one thousand. One thousand is expressed thus, 1000-by putting 1 in the fourth place, which is called the thousands' place. 17. The number of thousands is shown by the figure in the fourth place. 2000 two thousand Thus : 6000 six thousand 4000 four thousand 8000 eight thousand 9000 nine thousand 18. Ten thousand requires five figures to express it-10000. The fifth place is called that of ten thousands. 19. A hundred thousand requires six figures to express it-100000. The sixth place is called that of hundred thousands. 16. What is the greatest number that can be expressed with three figures? What comes next to 999? How is one thousand expressed? What is the fourth place called?-17. By what is the number of thousands shown? Give examples.-18. How many figures are required to express ten thousand? What is the fifth place called?-19. How many figures are required to ex press a hundred thousand? What is the sixth place called? 20. We have now had six places named :-units, tens, hundreds, thousands, ten thousands, hundred thousands. These six places are divided into two. Periods, of three figures each. The first Period is that of units; the second, that of thousands. 21. The second period is that of thousands. To express a given number of thousands, write the number in the second period. If there are no figures for the units' period, supply naughts. EXAMPLES.—Write four hundred and twenty-three thousand. To do this, write four hundred and twenty-three, as already shown-423-for the second period. Supply naughts for the units' period, and we have the required number423,000. So we write seventeen thousand, Six hundred and twenty thousand, 17,000. 501,000. 620,000. If there are numbers corresponding to the places of the units' period, set them there in stead of naughts. Forty-three thousand, two hundred and ninety, 43,290. Seven thousand, one hundred and five, 7,105. One hundred thousand, and sixty-seven. (As there are no hundreds in the units' period, supply 0.) 100,067. 20 Name the first six places in order. How are these six places divided? What is the first period called? What is the second period called? Name the places of the first period. Name those of the second period -21. How are we to express a given number of thousands? What must be done, if there are no figures for the units' period? Learn how to write the examples given. THE ARABIC NOTATION. 11 EXERCISE IN NOTATION. Write the following numbers in figures:1. Five hundred and nine thousand. 2. Sixty-three thousand, two hundred and seven. 3. Eleven thousand, one hundred and eleven. 4. Seven hundred thousand and seventy. 5. Six thousand. Six hundred thousand. 6. Forty-three thousand and thirty-four. 7. Five hundred and twelve thousand, seven hundred. 8. Eighty thousand, eight hundred and eight. 9. Nine hundred and ninety-nine thousand. 10. Write the greatest number that can be expressed with three figures; with four figures; with five figures; with six figures. MILLIONS, BILLIONS. 22. The third period is that of millions. It consists of three places,-millions, ten mil lions, hundred millions. EXAMPLES.-Two hundred million, Four hundred and one million, Seventy million, five hundred thousand, Six million, seventeen thousand, and seven, 200,000,000. 401,000,000. 70,500,000. 6,017,007. 23. The fourth period is that of billions. It consists of three places,―billions, ten billions, hundred billions. EXAMPLES.-One hundred and two billion, Four billion, twenty million, and six, 102,000,000,000. 11,000,011,002. 4,020,000,006. 22. What is the third period? Of how many places does it consist? Name them.-23. What is the fourth period? Of how many places does it consist? Name them. SUMMING UP. 24. Name the periods in order, beginning at the Name the places, beginning at the right. 10 units make 1 ten. 10 tens make 1 hundred. Hence, removing a figure one place to the right, diminishes its value ten times; removing it one place to the left, increases it ten times. 25. RULE.- Write billions in the fourth period, millions in the third, thousands in the second, units in the first, filling the vacant places with naughts, so as to have three places in each period. EXERCISE IN NOTATION. Write the following numbers in figures, placing units under units, tens under tens, &c.: 1. Four hundred and seventy-one billion, six thousand. 2. Ninety billion, three million, two thousand and four. 3. Eight hundred million, sixty thousand, one hundred. 24. What is the effect of removing a figure one place to the right? What is the effect of removing it one place to the left?-25. Give the rule for notation. |