5.2.5 DECIMAL FRACTIONS, LII. Q. When such fractions as these occur, viz. Ya Thor 18%, bow is a unit suppose 1 to be divided ! A. Into 10 equal parts, called tenths; and each tenth into 10 otherequal parts, called hundredths, and each hundredth into 10 more equal parts, called thousandths, &c. Q. How is it customary to write such eapressions ? A. By taking away the denominator, and placing a comma before the numerator. Let me see you write duwe, in this manucr, por po 1956, A. From the Latin word decem, signifying ten; because they increase and decrease in a tenfold proportion, like whole numbers. Q. What are all other fractions called ! Q. In whole numbers, we are accasionied to call the right-hand figure, units, from which we begin to rackou atmcrate; hence it was fount convenient w make iht, masine pince a starting point in deci. : mals; and to do this, we make use of a coinma; wliat, then, is ube use of this comma ? A. It merely shows where the units' place is. Q. What is the first figure at the right of the separatrix called ? andths, the fourth ten thousandths, and 80 on, o the numeration of whole numbers. Let me see you write down again to in the form of a decima. Q. As the first figure at the right of the separatrix is lewiha, riting down Ifo, tben, where must a cipher be placed ! A. In the tenths' place. A. ,05. Write down τσσ, τ8σ, τόσο A. By placing 2 ciphers at the right of the Heparatrix, that is, before the 7. Let me see you write it down. A. Because in Toro, the 2 is thousandths; con equently, the 2 must be thousandths when writ en down in decimals. Q. What does ,3 signify ! A. Q. What does ,06 signify ! Q. Now, as to et, and as multiplying ito by 10 prodana Polo, which is also equal to 1, how much len in value is ,06 than de A. Ten tiines. Q. Wty? A. Because the parts in ito arc ten times smaller than in ; and, as the numerator is tho rame in both expressions, consequently, the value is lessencd 10 times. Q. How, ther, do decimal figures decrease in value for the heat dwards the rigbt 1 A. In a tenfold proportion. Q. We have seen that ,5 is 10 times as much in value u ,00, Hoi what effect, then, does a cipher have placed at the lek decimals! A. It decreases their value in a tenfold proportion. Q. Since decimals decrease from the left to the right in a tenfeld proportion, how, then, must they increase from the right to ibe leni A. In the same proportion. Q. Since it was shown, that ,5 = M; ,25= o ; what, then Brill 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 slano and change them into a common or vulgar" fraction, by placing their proper deuominators under each, viz. ,6,75 ,005 ,62 ,0225 ,37. Q. ,25 is pos= }, and ,5 is Yo = ; which, then, is the most be alue, 25 or ,51 Q. By what, then, is the value of any decimal figures determined i A. By their distance from the units' place, a separatrix. Q. When a whole number and decimal are joined together, the Q. As any whole nunber may be reduced to tenths, hundredthy, dhousandths, &c. by anuexing ciphers, (for mulvplying by 10, 100, dve. tus, 5 is 50 tenths, 500 hundredths, &c.; bow, iben, may any mixed muumber be read, as 25,4 ? A. 254 tenths, giving the name of the decimal to all the figures. Q. How is 5,36 read I Q. What would 515 whousandths be, written la the form of oral A. +18.. This is evident from the fact, that 13! (an improper fractiont modared to a mixed vumber again, is equal to 5.125. The pupil may learn the names of any decimal expression, a los bon-millionths, also how to read or wriie decimals, com ubo fallowing (bilo: . Ho= 5 • read 5 Tenuks. To=...,06 read 6 Hundredihs. 1880 ,025. read 25 Thousandths. %=...,1328. read 1328. Ten-Thousandik 7%=..7,8. read 7, and 8 Tenths. Ooofoor = 6,000009. need 6, and 9 Millionthes 26736 26,25 • need 26, and 25 Hundredet Brooboor=..3,0000008 read 3, and 8 Ten-Millionthia 365=365,0000000 read 365. . Exercises for the Slate. Write in decimal form 7 tenths, 42 hundredths, 62 and 2 tandredths, 7 and 426 thousandths, 24 thousandths, 3 ten-thoa. uandths, 4 hundredths, 2 ten-thousandths, 3 millionths. Write the fractional part of the following numbers in the form of decimals, viz. 670, toy, 6216, 21%, 3160, 2621066 21835, 2Ισσσσσ, 45τσσσσσσ, 71σσσσσ, τσόσσ. Write the following decimal numbers in the form of vulgar & common fractions, then reduce them to their lowest terms by TXXXVII.; thus, 2,5 =216=24 in its lowest terms. 1. 45,5. A. 454. 7. 6,28. A. 675. 2. 9,25. A. 97 8. 6,005. A. 6. do . 8. 23,75. 4. 237 9. 3,00025. A. 3700 4. 11,8. A. 114 10. 6,08. 4 A. 6.3. 6. 19,9. A. 1936 11. 9,2. A. 95. 25,255 A. 25.06. 12. 7,000005. A. 7 godina Q. Whal money is adapted to decimal rules! A. As 10 dimes make a dollar, and 10 cents dime, &c., dimes are 10ths of a dollar, cents aro 100ths, and mills are 1000ths of a dollar. Q. How are 3 dollars 2 dimes 4 cents and 5 mills written ? ADDITION OF DECIMALS. I LIII. Q. As we have seen that decimals increase from night to left n the same proportion as units, lens, hundreds, &c., born Non, may all the operations of decimals be perforined ? A. As in whole numbers, Note.-The only dimenlty which ever arises, consists in determining where ha decimal point ought to be placed. This will be noticed in its proper place. 1. A merchant bought 570 barrels of rice at one time fa $27% o, at another pos of barrel for $4,255, at another 10on of a barrel for $, and at another of a barrel for $21030; how many barrels did he buy in all? and what did they cost him? OPERATION. As we have seen Barrels. Dollars that decimals cor 5,2 27,825 respond with the do 4,255 nominations of Fed erał Money, hence 0,72 we may write the de 189 2,627 cimals down,placing diines ander dimes, Ans. 6,988 barrels, for $35,427 cents under cents, &c., that is, tentbs under tenths, hundredths under hundredths, &c., and add these pas in Addition of Federal Money. From these illustrations we derive the following RULE. A. Tenths under tenths, hundredthe nude hundredths, and so on. Q. How do you proceed to add 1 ,62 |
