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1 7. Reduce 13 to a decimal. Thus, 13)1.00(.076923 &c. Answer. 90 12O 30 40 I
8. Reduce # to a decimal. Ans. .5,
RULE I. Reduce the given number to a fraction of the integer of which it is to be made a decimal, by Art. 185. II. Reduce this fraction to a decimal by the last rule".
13. Reduce 2s. 6d. to the decimal of a pound.
14. Reduce 14t. 14lb. to the decimal of a cwt.
* The foundation of this rule is sufficiently obvious without explanation. VOL. I. 2
16. Reduce 5s, to the decimal of a pound. Ans. 25l. 17. Reduce 3s.6d. to the decimal of a guinea. Ans...1666 &c. guinea. 18. Reduce 3oz. 5dwts. to the decimal of a lb. troy. Ans. .27.083 &c. lb. 19. Reduce 2r. 20p. to the decimal of an acre. Ans. .625 acre. 235. When the given quantity is of several denominations. RULE I. Write all the given denominations in a line under each other, beginning with the least, and proceeding in order up to the greatest. II. On the left of each, place that number for a divisor which will reduce it to a decimal of the next superior denomination. III. Divide each of the denominations, together with the decimals which arise, by its proper divisor, and the last quotient will be the decimal required". 20. Reduce 4s. 6d.; to the decimal of a pound.
OPERATION. Erplanation. 4 3.00 I put down 3 farthings first, 6d. next, and 4s. ~~ last; opposite these on the left I place 4, 12, and 126.75 20, being respectively the divisors which will re
20 4.5625 duce each to decimals of a superior denomination; I then divide each line, ciphers being subjoined .228 125l. Ans, where they are required. 21. Reduce 53 4329 Igr. to the decimal of a lb. 2O 1.OO 3|2.05 8|4,68333333 25.58541666 Tö451.8 lb. Answer.
* By this process the least denomination is reduced to a decimal of the next superior denomination, as is obvious from the foregoing rule; this latter denomination, with the said decimal subjoined, is reduced to a decimal of the next superior denomination; this again with its decimal to a decimal of the next; and so on to the highest: for instance, in ex. 20, 3 is reduced to the decimal of a penny, by dividing the 3 by the 4; then 6d., with this decimal, (viz. 6.75,) is reduced to the decimal of a shilling, by dividing it by 12; lastly, the whole number, with this decimal, (viz. 4.5.325,) is reduced to the decimal of a pound; which reductions are true, according to Art, 233; and the same of other examples: wherefore the rule is manifest.
236. To reduce a decimal to its proper quantity.
Rule I. Multiply the given decimal by that number which will reduce it to the next lower denomination, and mark off as many decimals from the product as there are decimal places in the given number.
II. Multiply these decimals by the number which will reduce them to the next lower denomination, and mark off decimals as before.
III. Proceed in this manner until you have reduced the decimals to the lowest denomination possible; then all the whole numbers being collected, and placed in order, will be the answer".
30. Reduce .228.125 of a pound to its proper quantity. OPERATION.
O *. Erplanation. -- I multiply the given decimal (of a pound) by 20, and 4,562500 s. mark off 6 places; these I multiply by 12, and mark off 12 6 places; these I multiply by 4, and again mark off 6
-- places. Then of the whole numbers, the 4 will evidently 6.750000 d. be shillings, the 6 pence, and the 3 farthings, which -4 together are the answer.
f This rule has its origin in the nature of Compound Division; for if the given decimal be considered as a remainder, the successive multiplications,
and marking off decimals, are equivalent to the successive reducing and dividing in that rule.
31. Reduce 7583 of a lb. troy to its proper quantity.
32. Reduce .159375 of a pound to its proper quantity. Ans, 3s. 2d.;. 33. Reduce .625 of a shilling to its proper quantity. Ans. 7d.}. 34. Reduce .05854 of a guinea to its proper quantity. Ans. 1s. 2d.;. 35. Reduce .6875 of a yard to its proper quantity. Ans. 24r. 3n. 36. What is the value of .625 cwt. Ans. 24r. 14b. 37. Reduce .3375 of an acre to its proper quantity. Ans. 1r. 14p. 38. What is the value of .461 of a chaldron? Answer 16bu. 2pks. 39. What is the value of .857.14 of a month Ans. 3v. 2d. 23h. 59m. 53”.
237. PROM1scuous ExAMPLEs for PRACTIce.
1. What is the value of .135 + .243 × .312 - Ans. .210816.
2. What is the value of .0098 – .00098 x .542 Answer .0099708.
3. Required the value of 3.74 x 2.35 – 1.23. Ans. 7,559.
7. 4. Required the value of 1.35 x 3.5 + 0.19. Ans. 5.15565. 5. What is 2.04 × 4.5 – 2.95 equal to 2 Ans, 3.162. 6. What is 123 + .94 x 2.12 – 89 equal to? Ans. 3,7104. 7. What is 123-F 94 x 2.12 – 89 equal to Ans. 2.6691. 8
. Find the value of 3.4 – 2.5 x .12 + 5.1 — .12. Aus. 4.578.
a pound, to be reduced to its proper quantity. Ans. 131, 19s. 9d,'.006.
13. Find Ans. 7.380361 &c.
being the decimal of
238. PROPORTION, or, THE RULE OF THREE
RULE. Reduce the first and third terms to decimals of the same denomination, and the second to a decimal of the greatest denomination mentioned; then state the question, and proceed as in the Rule of Three in Vulgar Fractions: the result will be of the same denomination with the second term, and (if a decimal) must be reduced to its proper quantity*.
ExAMPLEs. 3 1. If 8 of a cwt. of pimento cost 31, 2s. 6d. what is the value
Stating. OPERATION. 3.125 x 1.625 5,078.125 s 375 TT T.375 = 13.54166 = 131. 10s. 9d.; .99 &c. Answer. Earplanation.
Having reduced the first and third terms to decimals of a cwt. and the second to the decimal of a pound, I state the question, and, finding that the answer
s The rules of Proportion in whole numbers, vulgar and decimal fractions, depend all on the same principles; they differ only in the different modes of operation peculiar to each of these three kinds of numbers,