hundredths. (a) 7 = thousandths. (b) Change .275 to a common fraction and reduce it to its lowest terms. (c) .375. (d) .425. (e) .575. Review pages 133 and 143. (f) .625. (g) Find the cost of 6.28 acres of land at $2.75 an A.* (h) Find the cost of 3.46 tons of coal @ $6.75 a ton. (i) Divide 6.25 by 5. (6. 25+ 5 units.) (6.25 5 tenths.) (6.25÷ 5 hundredths.) (36 divided by 5 units.) (36.0 ÷ 5 tenths.) (36.005 hundredths.) (36.000 5 thousandths.) (57.26 divided by 7 units.) (57.2'67 tenths.) (57.267 hundredths.) (57.2607 thousandths.) (67.5 divided by 25 units.) (67.5 ÷ 25 tenths.) (67.5025 hundredths.) (67.500 25 thousandths.) ÷ (25 units in 6 units = 0., etc.) (6.7'5 ÷ 25 tenths.) == *Require the pupil to put the work on the blackboard and to explain by telling (1) the cost of 1 hundredth of an acre; (2) of 8 hundredths; (3) of 1 tenth; (4) of 2 tenths; (5) of 1 acre; (6) of 6 acres; (7) of 6.28 acres. How many decimal places in the product? How many in the multiplicand? How many in the multiplier? PART II. ΝΟΤΑΤΙΟΝ. 1. The expression of numbers by symbols is called notation. 2. In mathematics two sets of symbols are employed to represent numbers; namely, ten characters-1, 2, 3, 4, 5, 6, 7, 8, 9, 0-called figures; and the letters a, b, c, d, X, Y, Z. NOTE. The figures from 1 to 9 are called digits. The term significant figures is sometimes applied to the digits. The tenth character (0) is called a cipher, zero, or naught. THE ARABIC NOTATION. 3. The method of representing numbers by figures and places is called the Arabic Notation. It is the principle of position in writing numbers that gives to the system its great value. Fourth place. First decimal place. Second place. Second decimal place. Third place. Units of the fourth order. Units of the second order. Primary units. Units of the first decimal order. Units of the second decimal order. 8.5 96 4. A figure standing alone or in the first place represents primary units, or units of the first order; a figure standing in the second place represents units of the second order; a figure standing in the third place represents units of the third order; a figure standing in the first decimal place represents units of the first decimal order, etc. 5. The following are the names of the units of eight orders: 6. In a row of figures representing a number (342.65), the figure on the right represents the lowest order given; the figure on the left, the highest order given. In general, any figure represents an order of units higher than the figure on its right (if there be one), and lower than the figure on its left (if there be one). 7. Ten units of any order equal one unit of the next higher order; thus, ten hundredths equal one tenth; ten tenths equal one primary unit, etc. 8. The naught, or zero, is used to mark vacant places; thus, the figures 205 represent 2 hundred, no tens, and 5 primary units. NOTE 1.-Observe that a figure always stands for units. If it occupies the first place, it stands for primary units; if it occupies the second place, it stands for tens (that is, units of tens); the third place, for hundreds; the first decimal place, for tenths; the second decimal place, for hundredths, etc. Thus, a figure 5 always stands for five-five primary units, five thousand, five hundredths, five tenths, according to the place it occupies. NOTE 2. In reading integral numbers, the primary unit should be, and usually is, most prominent in consciousness. Thus, the number 275 is made up of 2 hundreds, 7 tens, and 5 primary units; but 2 hundreds equal two hundred (200) primary units, and seven tens equal seventy (70) primary units; these (200 +70 + 5) we almost unconsciously combine in our thought, and that which is present in consciousness is 275 primary units. So in the number 125,246, there are units of six orders, which we reduce in thought to primary units, and say, one hundred twenty-five thousand two hundred forty-six primary units. NOTE 3.-In reading decimals, too, the primary unit should be prominent in consciousness. Thus, .256 is made up of 2 tenths, 5 hundredths, and 6 thousandths; but 2 tenths equal 200 thousandths, and 5 hundredths equal 50 thousandths; these (200 + 50 + 6) we combine in our thought, and that which should be present in consciousness is 256 thousandths of a primary unit. Write in figures: 9. EXERCISE. 1. Two hundred fifty-four thousand one hundred. 2. One hundred seventy-five and two hundred six thousandths. 3. Eighty-four and three hundred five thousandths. 6. Twenty-four thousand six hundred fifty-one. |