2. Divide,07567 by 2,32467, true to four decimal places, or three significant figures, the first being a cipher.

2,3.21467),07567 (,0326. Ans.

697

59

46

13

14

3. Divide 5,37341 by 3,74, true to four decimal places. 3,74)5,87341 (1,4367. Ans.

374

1633

1496

1374

1122

252

224

28

26

4. Divide 74,33373 by 1,346787, true to three decimal places.

Ans. 55,193.

5. Divide 87,076326 by 9,365407, true to three decimal places. Ans. 9,297.

6. Divide 32,68744231 by 2,45, true to two decimal places. Ans. 13,34.

7. Divide ,0046872345 by 6,24, true to five decima places. Ans. ,00075

SECTION 5.

REDUCTION OF DECIMALS.

Case 1.

To reduce a vulgar fraction to a decimal.

RULE.

Annex one or more ciphers to the numerator, and divide by the denominator; the quotient will be the answer in decimals.

To reduce numbers of different denominations to a deci mal of equal value.

RULE.

Set down the given numbers in a perpendicular column, having the least denomination first, and divide each of them by such a number as will reduce it to the next name, annexing the quotient to the succeeding number; the last quotient will be the required decimal.

EXAMPLE.

1. Reduce 17s. Sąd. to the decimal of a pound.

Ans. ,95

,25

,0125

2. Reduce 19s. to the decimal of a pound.

,225

,625

,9375

Case 3.

To reduce a decimal to its equal value in integers.

RULE.

Multiply the decimal by the known parts of the integer

EXAMPLE.

1. Reduce,9864583 of a pound to its equivalent value in integers.

,8864583

20

s. 17,7291660

12

d. 8,7499920

4

qr. 2,9999680

It is usual when the left hand figure in the remaining decimal exceeds five, to expunge the remainder, and add one to the lowest integer. Thus, instead of 17s. 8d. 2,999, &c. we may say 17s. 83d. Ans.

2. What is the value of ,75 of a pound?
3. What is the value of ,7 of a pound troy?

4. What is the value of ,617 of a cwt.?

Ans. 15s.

Ans. 8oz. 8dwt.

Ans. 2qr. 13lb. 1 oz. 10+dr. 5. What is the value of ,3375 of an acre?

Ans. 1 rood, 14per.

6. What is the value of ,258 of a tun of wine?

Ans. 1hhd. 2+gals.

7. What is the proper quantity of,761 of a day?

Ans. 18h. 15mi. 50,4sec.

3. What is the proper quantity of ‚7 of a lb. of silver?

Ans. 8oz. 8dwt.

What is the proper quantity of ,3 of a year?

Ans. 109d. 13h. 48mi.

10. What is the difference between ,41 of a day and,16 of an hour? Ans. 9h. 40mi. 48sec. 11. What is the sum of,177. 19cwt. 17qr. and 7lb. ? Ans. 3cwt. 2qr. 15,54lb.

Promiscuous Questions in Decimal Fractions.

1. Multiply,09 by,009.

Ans. ,00081.

2. In,36 of a ton (avoirdupois) how many ounces?

Ans. 12902,4oz.

3. What is the value of,9125 of an ounce troy?

4. Reduce to a decimal.

Ans. 18dwt. 6gr. Ans. ,0127 nearly.

Ans. ,2368+nearly.

5. Reduce 2oz. 16dwt. 20gr. to the decimal of a pound

troy.

6. What is the length of ,1392 of a mile?

Ans. 1 fur. 4 per. 3 yds nearly. 7. What multiplier will produce the same result, as multiplying by 3, and dividing the product by 4?

Ans. ,75. Ans. ,0535714.

8. What decimal of 1cwt. is 6lb.
9. What part of a year is 109 days 12 hours?

Ans.,3. 10. In ,04 of a ton of hewn timber, how many cubic Ans. 3456. inches? 11. What is the value of of a dollar divided by 3?

Ans. 63 cents.

12. What is the value of ,875 of a hhd. of wine?

Ans. 55 gal. 0 qt. 1 pt. 13. What divisor, true to six decimal places, will produce the same result as multiplying by 222?

Ans. ,004504.

14. In,05 of a year, how many seconds, at 365 days 6 hours to the year? Ans. 1577880. 15. What number as a multiplier will produce the same result as multiplying by ,73 and dividing first by 3, and the Ans. ,973. quotient by,25? 16. What is the difference between,05 of a year, and,5 Ans. 2w. 2d. 18h. 42m.

of an hour?

17. In,4 of a ton,,3 of a hhd. and,8 of a gallon, how Ans. 964. many pints? 18. How many perches in ,6 of an acre; multiplied by Ans. 1,92.

,02 ?
19. What part of a cord of timber is 1 cubic inch?

Ans. ,000004+

20. What part of a circle is 28 deg. 48 minutes?

Ans. ,08.

PART IV.

PROPORTIONS.

THIS part of arithmetic which treats of propertions is very extensive and important. By it an almost innumerable variety of questions are solved. It is usually divided into three parts, viz. Direct, Inverse, and Compound.—The first of these is called the Single Rule of Three Direct, and sometimes by way of eminence the Golden Rule. The second is called the Single Rule of Three Inverse: and the last is called the Double Rule of Three. In all these, certain numbers are always given, called data, by the multiplication and division of which, the answer in an exact ratio of proportion to the other terms is discovered.

SECTION 1.

SINGLE RULE OF THREE DIRECT

In this rule three numbers are given to find a fourth, that shall have the same proportion to the third, as the second has to the first.

If by the terms of the question, more rcquires more, or less requires less, it is then said to be direct, and belongs to

this rule.

In stating questions in this rule, the middle term must always be of the same name with the answer required; the last term is that which asks the question, and that which is of the same name as the demand, the first. When the question is thus stated, reduce the first and third terms to the lowest denomination in either; and the middle term (if compound) to its lowest, and proceed according to the following

RULE.

Multiply the second and third terms together, and divide the product by the first; the quotient will be the fourth term, or answer, in the same name with the second.