Wride down Ibo, 1%, Ito Q: How would you write down in decimals Todo? 4. By placing 2 ciphers at the right of the separatrix, that is, beforo the 7. Let me see you write it down ? A. ,007. Q. Why do you write 2 down with 2 ciphers before it? A. Be cause in Togo, the 2 is thousandths ; consequently, the 2 muss be thousandths when written down in decimals. Q. What does ,5 signify? A. Po Q. Now, as Bo=, and as multiplying To by 10 produces So, which is also equal to 1, how much less in value is ,05 than ,5 ? A. Ten times. Q. Why? A. Because the parts in Ifo are ten times smaller than in B ; and, as the numerator is the same in both expres sions, consequently, the value is lessened 10 times. Q. How, then, do decimal figures decrease in value from the left towards the right ? A. In a tenfold proportion. Q. What does ,50 mean. A. 5 tenths, and no hundredths. Q. What, then, is the value of a cipher at the right of deci inals? A. No value. Q. We have seen that ,5 is 10 times as much in value as ,05, or Too; what effect, then, does a cipher have placed at the left of decimals ? A. It decreases their value in a tenfold proportion. Q. Sinco decimals decrease from the left to the right in a tenfold proportion, how, then, must they increase from the right to the left ? A. In the same proportion. R. Since it was shown, that ,5=M; ,25=, what, then, will always be the denominator of any decimal expression? A. The figure 1, with as many ciphers placed at the right of it as there are decimal places. Let me see you write down the following decimals on your slate, and change them into a common, or vulgar fraction, by placing their proper denominators under each, viz. ,5,05 ,005,62 ,0225 ,37. Q. „25 is fort, and ,5 is Bo=}; which, then, is tho most in value, ,25 or ,5? Q. By what, then, is the valug of any decimal figures distermined ? A. By their distance from the units' placo, or sepa Q. When a whole number and decimal are joined together, thus ; 2,5, what is the expression called ? A. A mixed number UPL matrix. hr dredths, 7 and 426 thousandtles, 24 thousandths, 3 ten-thors Q. As any whole number may be reduced to tenths, bun dredths, thousandths, &c. by annexing ciphers, (for niultiply ing by 10, 100, &c.) thus, 5 is 50 tenths, 500 hundredths, &c.; how, then, may any mixed number be read, as 25,4? A. 254 tenths, giving the name of the decimal to all the figures. Q. How is 25,36 read ? 1. 2536 hundredths. 2. What would 5125 thousandths be, written in the form of a vulgar or common fraction ? A. 11%. This is evident from the fact, that can improper fraction), reduced to a mixed number again, is equal to 5,125 The pupil may learn the names of any decimal expression, as far as ten-millionths, also how to read or write decimals, from the following TABLE. = 5 read 5 Tentos. 180= 06 read 6 Hundredths. 188=...,025 read 25 Thousandths. 1328 read 1328 Ten-Thousanatns 78=..7,8. read 7, and 8 Tenthis, 6100ouo=..6,00000 9. read 6, and 9 Millionths. 26.365.26,25 read 26, and 25 Hundredths 370008000=..3,0000008 read 3, and 8 Ten-Millionthe. 36533 6 5,000000 0 read 365. Exercises for the Slate. Write in decimal form 7 tenths, 42 hundredths, 62 and 23 sundheis A kundredths, 2 ten-thousandths, 3 millionths. WYritė the fractional part of the following numbers in th Hundreds. Ten-Millionths. Units. . 329 . . of decimals, viz. 670, 4, 6278, 27, 3187, 2621060, 321831, 2 Todood, 45 Tofu, 7701TU, 510tso Write the following decimal numbers in the form of ulgar or common fractions, then reduce them to their lowesterms by "XXXVII; thus, 2,5=28=21 in its lowest terms. 1. 45,5 A. 454 7. 6,28 A. 6,5 2. 9,25 A. 91 A. 6760 3. 23,75 A. 23 9. 3,00025 A. 3Toto 4. 11,8 A. 11% A. 675 5. 19,9 A. 1978 11. 9,2 6. 25,255 A. 25-1 | 12. 7,000005 A. 70'UO Q. What money is adapted to decimal rules ? A. Federal Money. Q. What is the money unit? A. The dollar. & How is it so adapted ? A. As 10 dimes make a dollar, and 10 cents a dime, &c., dimes are 10ths of a dollar, cents are 100ths, and mills are 1000ths of a dollar. Q. How are 3 dollars 2 dimes 4 cents and 5 mills written: 1. $3,245. A. 93 ADDITION OF DECIMALS. I LIII. Q. As we have seen that decimals increase from sight to left in the same proportion as units, tens, hundreds, &c., dow, then, may all the operations of decimals be performed 1. As in whole numbers. Note. The only difficulty, which ever arises, consists in deLormining where the decimal point ought to be placed. This will be noticed in its proper place. 1 A merchant bought 51% barrels of rice at one time for $27-308, at another sit of a barrel for $4,255, at another % of a barrel for $70%, and at another too of a barrel for $2167%; how many barrels did he buy in all ? and what dia they cost him? OPERATION As we have seen that decimals Barrels. Dollars. correspond with the denomina5,2 27,825 tions of Federal Money, herce ,62 4,255 we may write the decimals down, 278 0,72 placing dimes under dimes, ,89 2,627 cents under cents, foc., that is, tenths under tenths, hundredlhs Ans.6,988barrels for $35,427 | under hundredths, fc., and add dem up as in Addition of Federal Money From these illustrations we derive the following RULE. | How are the numbers to be written down ? A. Terths andor tenth :, hundredths under hundredths, and so on. II. How do you proceed to add ? A. As in Simple Addition. III. IVhere do you place the separatrix ? A. Directly under the separating points above. More Exercises for the Slate. 2. James bought 2,5 cwt. of sugar, 23,265 cwt. of hay, and 4,2657 cwt. of rice; how much did he buy in all ? A. 30,0307 cwt. 3. James is 14 years old, Rufus 1576, and Thomas 1675; what is the sum of all their ages ? A. 46,5 years. 4. William cxpended for a chaise $255, for a wagon $37-14, for a bridie $175, and for a saddle $1115 ; what did these amount to?" A. $304,455. 5. A merchant bought 4 hhds. of molasses; the first wnlained 621 gallons, the second 72 % gallons, the third 50 % gallons, and the fourth 55,705 gallons; how many gallons did he buy in ihe whole ? A. 240,6157 gallons. 6. James travelled to a certain place in 5 days; the first day he went 40% miles, the second 281,7 miles, the third 4210 miles, the fourth 22 roko miles, and the tith 2910% y miles, how far did he travel in all? 4. 162,0792 miles. 7. A grocer, in one year, at different times, purchased the fol lowing quantity of articles, viz. 427,2623 cwt., 2789,00065 cwt., 42,000009 (wt., 1,3 cwt., 7567,126783 cwt., and 897,62 cwt.; how much did he purchase in the whole year: 4.11724,309742 8. What is the amount of %, 25106, 67707, 24570001 1108, %J, 427T00000, 43, 1000, and 1925 ? A. 2354,492472. 9. What is the amount of one, and five tenths; forty-five, and three hundred and forty-nine thousandths; and sixteen hundredths ? A. 47,009. cwt SUBTRACTION OF DECIMALS. I LIV. 1. A merchant, owing $270,42, paid $192,625 how much did he then owe? OPERATION $270,42 For the reasons shown in Addition, we $192,625 proceed to subtract, and point off, as in Sub traction of Federal Money. Ans. $77,795 Hence we derive the following RULE. | How do you write the numbers down? A. As in Additice af Decimals. II. How do you subtract ? A. As in Simple Subtraction. III. How do you place the separatriz ? A. As in Addition of Decimals. More Exercises for the Slate. 1. Bought a hogshead of molasses, containing 60,72 gallons ; how much can I sell from it, and save 19,999 gallons for my own use ? A. 40,721 gallons. 2. James rode from Boston to Charlestown in 4,75 minutes, Rufus rodo the same distance in 6,25 minutes; what was the difference in the time? A. 1,5 min. 3. A merchant, having resided in Boston 6,2678 years, stated his age to be 72,625 yrs. Ilow old was he when he emigrated to that place. 4. 66,3572 yrs. Note. 'The pupil must bear in mind, that, in order to obtain the answer, the figures in the parentheses are first to be pointed off, supplying ciphers, if necessary, then added together as in Ado dition of Decimals. 4. From ,65 of a, barrel take ,125 of a barrel; (525) take ,2 of a barrel; (45) take ,45 of a barrel; (2) take , of a barrel; (5) take ,12507 of a barrel; (52433) take ,28 of a barrel ; (39) À 2,13933 barrels. 5. From 420,9 pipes take 126,45 pipes; (29445) tako ,625 of a pipe; (420275) take 20,12 pipes ; (40078) take 1,62 pipes , (41928) take 419,89 pipes; (101) take 419,8999 pipes; (10001). Ans. 1536,7951 pipes. MULTIPLICATION OF DECIMALS. TLV. 1. How many yards of cloth 'n 3 pieces, each piece containing 20-35 yards? OPERATION In this example, since multiplication is a 20,75 short way of performing addition, it is pl.in 3 that we must point off as in addition, viz. direcily under the separating points in tho Ars. 62,25 yds./ muda the multiplicana, and is geen two multiplicand; and, as either factor may be |