(2.) Divide 59 by 74571345, and let the quotient contain four places of decimals. (3.) Divide 17493 407704962 by 495 783269, and let the quotient contain four places of decimals. (4.) Divide 98-187437 by 8-4765618, and let the -quotient contain ten places of decimals. (5.) Divide 47194-379457 by 14.73495, and let the quotient contain as many decimal places as there will be -integers in it. REDUCTION OF DECIMAL FRACTIONS. Proposition 1. To reduce a vulgar fraction to a decimal fraction of equal value. RULE. Annex ciphers to the numerator till it be equal to, or greater than, the denominator: then divide by the denominator as in division of decimals, and the quotient will be the answer. Note. Mr. Colson, at page 162 of Sir Isaac Newton's Fluxions, gives the following method for reducing a fraction, having a prime number for its denominator, into a decimal. Let be proposed: then, by dividing in the common way, till the remainder becomes a single figure, we shall have03448, for the complete quotient; and this equation multiplied by the numerator 8, will give 27586, and, if this be substituted in the first equation for, we shall have 50344827586. Again, multiply the equation by 6, and it will give =2068965517; then, by substituting, as before, 03448275862068965517, &c. as far as you please. Prop. 2. To reduce numbers of different denominations, coins, weights, measures, &c. into decimals *. *The decimal tables of coin, weights, measures, &c. are calculated by the rules given in this proposition; thus in Table I. 19 shillings= 95, &c. The use of the tables is shewn in the 9th example. RULE I. Reduce the given money, weight, &c. into the lowest denomination mentioned for a dividend: then reduce the integer into the same denomination for a divisor: the quotient produced by this division will be the decimal required. RULE II. Write the given denominations, or parts, regularly under each other, proceeding from the lowest denomination to the highest; let these be the dividends. Opposite to each dividend, on the left-hand, place such a number for a divisor as will reduce it to the next superior name, and draw a line between them. Begin to divide with the uppermost numbers, and write the quotients of each, as decimal parts, on the right hand of the dividend next below it. Divide this mixed number by its divisor, and so on till they are all used, the last quotient will be the decimal required. Prop. 3. To find the value of any decimal fraction in the known parts of an integer. RULE. Multiply the given decimal by the number of parts contained in the next inferior denomination; and, from the right-hand of the product, point off so many figures as the given decimal consists of. Multiply the remaining decimals by the parts in the next inferior denomination, and from what results cut off as before. Proceed thus till you have brought out the least known parts of the integer, and then the several denominations, on the left-hand of the decimal points, will express the value of the decimal. (3.) Reduce 23 to a decimal fraction. (4.) Reduce to a decimal. of of to a decimal. (5.) Reduce (6.) Reduce 15 to a mixed decimal. (7.) Reduce to a decimal. (9.) Reduce 188. 9ąd, to the decimal of a pound. (10.) Reduce 7s. 5 d. to the decimal of a pound. (11.) What decimal part of a pound is three half-pence? (12.) Reduce 4s. 7d. to the decimal of a pound. (13.) Reduce 1 oz. 11 dwt. 3 gr. to the decimal of a pound Troy. (14.) Reduce 24 grains to the decimal of an ounce Troy. (15.) Reduce 5 oz. 4 dr. Avoirdupois to the decimal of a pound Troy. (16.) Reduce 3 cwt. 1 qr. 14 lb. to the decimal of a ton. (17.) Reduce 2 qr. 15 lb. to the decimal of a hundredweight. (18.) Reduce 5 lb. 10 oz. 3 dwt. 13 gr. Troy to the decimal of a hundred-weight Avoirdupois. (19.) Reduce 1 qr. 1 n. to the decimal of a yard. (20.) Reduce 2qr. 3 n. to the decimal of an English ell. (21.) Reduce 14 yds. 2 ft. 6 in. to the decimal of a mile. (22.) What decimal part of an acre is 1 r. 37 poles? (23.) What decimal part of a hogshead of wine is 2 qts. 1 pint? (24.) Reduce 3 bush. 3 pks. to the decimal of a chaldron of 32 bushels. (25.) What decimal part of a year is 3 w. 6d. 7 hrs., reckoning 365 d. 6 hrs. a year? K (26.) Reduce 2.45 shillings to the decimal of a £. (27.) Reduce 1.074 roods to the decimal of an acre. (28.) Reduce 176.9 yards to the decimal of a mile. Examples to Prop. 3. (29.) Required the value of 03125 of a pound sterling. (30.) What is the value of 7575 of a pound sterling. (31.) Required the value of 75435 of a shilling. (32.) What is the value of (33.) What is the value of (34.) What is the value of (35.) What is the value of dupois? 375 of a guinea? 02575 of a pound Troy. (36.) Required the value of (37.) Required the value of 075 of a yard. (38.) Required the value of 475 of an English ell. (39.) What is the value of '04535 of a mile? (40.) What is the value of 6375 of an acre? (41.) What is the value of 574 of a hogshead of beer? (42.). What is the value of 4285 of a year? (43.) Required the sum of of a shilling. (44.) Required the sum of of a yard. 475 of a pound and 375 573 of an inch and 751 (45.) Required the difference between 5 of a mile and 375 of a furlong. (46.) of a ton. Required the sum of 625 of a cwt. and •20835 (47.) Required the sum of 175 ton, 195 cwt. 145 qr. and 15 lb. (48.) Required he sum of 575 lb. Troy and 845 oz. |