Exercises. Write in figures arranged in columns: 1. The numbers between forty-five and sixty-three. THOUSANDS. 25. Ten hundreds are called ONE THOUSAND, which forms a unit of the fourth order, and is written 1000. Therefore, to express one thousand, two thousand, three thousand, etc., we write the figures denoting their number, with three ciphers at the right. Thus, we write, 26. Ten thousands are called ONE TEN-THOUSand, which forms a unit of the fifth order, and is written 10000. Also, Two ten-thousands, or twenty thousand, is written 20000. Three ten-thousands, or thirty thousand, is written 30000, and so on. 27. Ten ten-thousands are called ONE HUNDRED-THOUSAND, which forms a unit of the sixth order, and is written 100000. Also, Two hundred thousand is written 200000; three hundred thousand is written 300000; and so on. What are ten hundreds called? What unit does one thousand form? How are one thousand, two thousand, etc., written? What are ten-thousands called? What unit do ten-thousands form? What are ten ten-thousands called? What unit do ten ten-thousands form? where the figures express 3 hundred-thousands O ten-thousands 6 thousands 5 hundreds 7 tens 4 units, or three hundred six thousand five hundred seventy-four. 29. In general, in writing a number by figures, we write each of the figures in the order of its units, and note the absence of a significant figure, in an order, by a cipher. Thus, Five thousand twenty, or 5 thousands 0 hundreds 2 tens 0 units, is written 5,020. What are orders of figures? To what do they correspond? How are orders of figures separated for convenience in reading? From what does each period take its name? Name the first two periods. Name the first six orders of units. How do we write figures in expressing numbers? 28. The ORDERS OF FIGURES are the positions they occupy with reference to each other, when written side by side. Each figure expresses an unvarying number of units, and the order of the figure determines the size or name of the units. For convenience, in reading numbers expressed by figures, their orders are separated into groups, of three figures each, called PERIODS. Each period takes its name from its right hand order. The three orders of any period, beginning at the right, express respectively units, tens, and hundreds of that period. Thus, we have, Exercises. Write in figures and read: 1. Three units of the fourth order, with no units of the third order, two units of the second, and one unit of the first order. Ans. 3,021; read, three thousand and twenty-one. 2. 5 hundred-thousands 3 ten-thousands and 4 thousands 6 hundreds and 4 tens. Ans. 534,640; read, five hundred thirty-four thousand six hundred and forty. 3. 415 in the second period, and 405 in the first period. Ans. 415,405; read, four hundred and fifteen thousand four hundred and five. 4. 207 in the second period and 0 in each order of the first period. 5. 38 thousands 3 hundreds 5 tens and 2 units. 6. 6 hundred-thousands 5 ten-thousands with seven units of the first order. 30. The Arabic system of notation is based upon the following GENERAL PRINCIPLES. 1. Numbers may be expressed by writing figures so as to denote their orders of units. 2. Ciphers written with other figures denote or mark the orders in which units are omitted. 3. Ten units of any lower order are always equal to one of the next higher. That is, ten units make one ten, ten tens make one hundred, ten hundreds make one thousand, and so on. Hence. 4. Each removal of a figure an order towards the left, makes the value expressed ten-fold. Give the first general principle. The second. The third. The fourth. SCALE OF NUMBERS. 31. A Scale of Numbers is the number or numbers expressing the law of relation between their different units. 32. In numbers, where ten units of any lower order always make one of the next higher, the scale is ten, and uniform. For this reason, the system of numbers in general use has been called from decem, the Latin for ten, the DECIMAL SYSTEM OF NUMBERS. 33. The common, or French method of Numeration, is exhibited in the following 18th. Hundreds co 17th. Tens -16th. Units 15th. Hundreds 14th. Tens 13th. Units 12th. Hundreds 11th. Tens 8th. Tens 5th. Tens where the 3, 1 5 4, 2 0 5, 6 3 8; figures express four hundred thirty-one QUADRIL LIONS, five hundred sixty-two TRILLIONS, seven hundred ninety-three BILLIONS, one hundred fifty-four MILLIONS, two hundred five THOUSANDS, six hundred thirty-eight. A dot (.), called the Decimal Point, is used to mark the units' place, by being written at the right of the units' figure. Thus, 8. is read eight units. What is a Scale of Numbers? What is the scale of numbers in which ten anits of a lower order always make one of the next higher? Beginning at the right, name the periods in the table. The orders. The value expressed of The periods above Quadrillions, in their order, are Quintillions, Sextillions, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, Tredecillions, Quatuordecillions, Quindecillions, Sexdecillions, Septendecillions, Octodecillions, Novendecillions, Vigintillions, etc. 34. To read numbers expressed by figures. 1. Let it be required to read 7693254. Pointing off the given figures into periods, beginning at the units place, we have 7,693,254. The third period is 7 millions, the second period is 693 thousands, the first period is 254 units; therefore, the whole reads, seven million six hundred ninety-three thousand two hundred fifty-four. Hence, the RULE. Beginning at the units' place, point off the given expression into as many periods as possible, of three figures each. Then, begin at the left and read each period, giving after each, excepting the last, the name of the period. The name of units' period is not given in reading figures, since it is readily understood; and the decimal point, when not written, is also understood. Name the periods in their order above Quadrillions. Repeat the Rule. Why is not the name of units' period given in reading figures? |
