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3. Divide 12,82561 by 3,01.
Ans. 4,261, 4. Divide 33,66431 by 1,01.
Ans. 33,331. 5. Divide ,010001 by ,01.
Ans. 1,0001. 6. Divide 8,2470 by ,002.
Ans. 4123,5. NOTE. $ 170. When any decimal number is to be divided by 10, 100, 1000, &c. the division is made by removing the decimal point as many places to the left as there are O's in the divisor; and if there be not so many figures on the left of the decimal point, the deficiency must be supplied by prefixing ciphers.
,2769 27,69 divided by
10000 ,002769 Note 2. § 171. When there are more decimal places in the divisor than in the dividend, annex as many ciphers to the dividend as are necessary to make its decimal places equal to those of the divisor; all the figures of the quotient will then be whole Rumbers, 169.
Ex. 1. Divide 4397,4 by 3,49.
e annex one 0 to 3,49)4397,40(1260 the dividend. Had it
349 contained no decimal
907 place we should have
698 annexed two.
2. Divide 2194,02194 by ,100001.
Ans. 21940. 3. Divide 9811,0047 by ,325947.
Ans. 30100. 3. Divide ,1 by ,0001.
Ans. 1000. NOTE 3. § 172. When it is necessary to continue the division farther than the figures of the dividend will allow, we may annex ciphers and consider them as decimal places of the dividend.
Ex. 1. Divide 4,25 by 1,25.
In this example, we annex 1,25 4,25(3,4 one 0 and then the decimal
3,175 places in the dividend will ex
500 ceed those in the divisor by 1.
Ans. 3,4 2. Divide ,2 by ,06.
We see in this example ,06),20(3,33+ that the division will never
18 terminate. In such cases
20 the division should be car
18 ried to the third or fourth
20 place, which will give the
18 answer true enough for all
20 practical purposes, and the sign + should then be written, to show that the di. vision may be still continued. 3. Divide 37,4 by 4,5.
QUESTIONS. $ 165. What parts of unity can be added together ? How must the figures be set down? How is addition of decimals
w do you set down the numbers ? How do you
o you point off in the sum ?
i § 166. What does subtraction of decimals teach ? How do you set down the numbers ? How do you subtract thom? How do you point off in the remainder ?
$ 167. How many decimal places will the product of two decimals contain? When there are not so many in the product, what do you do? What is the rule for multiplication of decimals ?
$ 168. How do you multiply a decimal by 10, 100, 1000, &c.
$ 169. What is division of decimals? How many places of decimals must the dividend contain ? How do you find the number of places in the quotient ? What is the rule for divi. sion of decimals ?
$ 170. How do you divide a decimal by 10, 100, 1000, &c.
§ 171. If the decimal places in the divisor exceed those in the dividend what do you do? What will the figures of the quotient be?
§ 172. How do you continue the division after you have brought down all the figures of the dividend ? What sign do you place after the quotient ?
IN THE FOUR PRECEDING RULES.
1. A merchant sold 4 parcels of cloth, the first contained 127 and 3 thousandths yards; the 2d, 6 and 3 tenths yards; the 3d, 4 and one hundredths yards; the 4th, 90 and one millionth yards : how many yards did he sell in all ?
Ans. 227,31300lyd. 2. A merchant buys three chests of tea, the first contains 60 and one thousandth lb.; the second 39 and one ten thousandth 16.; the third, 26 and one tenth lb. : how much did he buy in all ?
Ans. 125,101115. 3. Whai is the sum of $20 and three hundredths; $4 and one tenth, $6 and one thousandth, and $18 and one hundredth ?
DIVISION OF DECIMAL FRACTIONS.
4. A puts in trade $504,342; B puts in $350,1965; C puts in $100,11; D puts in $99,334; and E puts in 9001,32: what was the whole amount put in?
Ans. $10055,3025. 5. B has $936, and A has $1 three dimes and one mill: how much more money has B than A ?
Ans. $934,69,9. 6. A merchant buys 37,5 yards of cloth, at $1,25 per yard : how much does the whole come to ?
Ans. $46,87,5. 7. A farmer sells to a merchant 13,12 cords of wood at $4,25 per cord, and 13 bushels of wheat at $1,06 per bushel : he is to take in payment 13 yards of broadcloth at $4,07 per yard, and the remainder in cash : how much money did he receive ?
Ans. $16,63. 8. If 12 men had each $339 one dime 9 cents and 3 mills : what would be the total amount of their money ?
Ans. $4070,31,6. 9. If one man can remove 5,91 cubic yards of earth in a day: how much could 19 men remove?
Ans. 112,29yd. 10. What is the cost of 8,3 yards of cloth at $5,47
Ans. $45,40,1. 11. If a man earns one dollar and one mill per day: how much will he earn in a year?
Ans. $365,36,5. 12. What will be the cost of three hundred and 75 thousandths of a cord of wood, at $2 per cord ?
Ans. $0,75. 13. A man leaves an estate of $1473,194 to be
've divided among 12 heirs : what is each one's
REDUCTION OF VULGAR FRACTIONS TO DECIMALS. 181
REDUCTION OF VULGAR FRACTIONS TO
DECIMALS. $ 173. The value of every vulgar fraction is equal to the quotient arising from dividing the numerator by the denominator, 58.
Thus, s=4. Here the 1 cannot be divided by the 2; but 1 is equal to 10 tenths, equal to 100 hundredths, or equal to 1000 thousandths, &c.: hence we shall have =41=440=4,5. Therefore, to reduce a vulgar fraction to a decimal we have the fole lowing
I. Annex one or more ciphers to the numerator and then divide by the denominator.
II. If there is a remainder, annex a cipher or ciphers, and divide again, and continue to annex ciphers and to divide until there is no remainder or until the quotient is sufficiently exact : the number of decimal places to be pointed off in the quotient is the same as the number of ciphers used ;-and when there are not so many, ciphers must be prefixed. Ex. 1. Reduce il to its equivalent decimal.
Ans. ,25 and ,00797+. 3. Reduce H, 37, todo, and also to decimals,
Ans. ,025; ,692+ ; ,003; ,000 4. Reduce ; and ting to decimals.
Ans. ,5 a