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Tale

Number of Places you would have in the Fraction) to the
Decimal fought.

If the Reader thinks proper, he may omit the following Method of finding the Value of a Decimal Fraction, and proceed to the next Article.

But, in the Fraction of a Pound Sterling, and in FootMeasure, there is a much readier Way to find their Value than by the common Method of Reduction: Thus, in the Fraction of a Pound, the firft Figure next the Dot being doubled is Shillings: And, if the fecond Figure is lefs than 5, reckon that and the next as fo many Farthings; only, if they are more than 13, abate 1, or, more than 38, abate 2: And the Farthings thus found, being added to the Shillings before found, will be the Value of the Decimal Fraction.

But, if the fecond Figure fhould be more than 5, then take 5 from it, for which add 1 Shilling to the Shillings before found: And 5 being taken from the fecond Figure, to the Remainder, if there is any, join the third Figure, and reckon them as Farthings; if they are above 13, abate 1, or, if above 38, abate 2, as before: And the Farthings thus found, being added to the Shillings before found, will be the Value of the Decimal Fraction.

If the Fraction is of four Places, the Value may be ascertained a small Matter nearer, by taking in the fourth Figure; but, as this is not fo neceffary to my prefent Defign, I shall omit it, and proceed to Examples, to illuftrate what has been faid.

45.

The Value of .2 of a Pound is
The Value of .5 of a Pound is 105.

The Value of 7 of a Pound is 14 S.

The Value of .9 of a Pound is 18s. this being no more but to double the first Figure.

The Value of .25 of a Pound is 5s. For the 2 being doubled is 4s. and the fecond Figure being a 5 is Is. and this being added to the 45. it makes 5 s. for the Value of .25 of a Pound.

The Value of .45 of a Pound is 9s. For the 4 being doubled is 8s. to which adding 1 for the 5, it makes 9 s.

The Value of .75 of a Pound is 15s.

And the Value of .95 of a Pound is 19s.

The Value of .412 of a Pound is 8s. 3 d. For the 4 being doubled is 8s. then, the fecond Figure being under 5, and the second and third Figures being less than 13, the 12 are

M 2

reckoned

reckoned as Farthings, which is 3d. Whence the Value is 8s. 3d.

The Value of 519 of a Pound is 10s. 4d.

For the 5 being doubled is 10s. then abate I from the 19, and there remains 18, which are Farthings: Whence the Value is 10s. 4 d. 4.

The Value of 741 of a Pound is 145. 9d. : For the 7 being doubled is 145. then from the 41 abate 2, and there remains 39, which are Farthings: So that the Value is 14s. 9 d. 1.

The Value of .561 of a Pound is 11s. 2d. : For the 5 being doubled is 10s. then, the fecond Figure being more than 5, fubtract 5 from it, for which add I to the Shillings; and, when 5 is taken from the 6, there remains I ; to which join the third Figure, 1, and it makes 11, which are Farthings: Hence the Value is 11s. 2 d. 4.

To find the Value of .785 of a Pound: The 7 being doubled is 14s. then fubtract 5 from the 8, and for it add I to the Shillings; and, 5 being fubtracted from the 8, there remains 3 to which joining the third Figure, 5, it makes 35, from which abate I, and there remains 34, which are Farthings: Whence the Value is 15s. 8d.

To find the Value of .895 of a Pound: The 8 being doubled is 16 s. then fubtract 5 from the 9, for which add I to the Shillings; and, 5 being fubtracted from the 9, there remains 4, to which joining the third Figure, 5, it makes 45, from which abate 2, and there remains 43, which are Farthings: So that the Value is 17 s. 10d. 4.

If the Reader has an Inclination to fee how near thefe, or any other Conclufions of this Sort, come to the Truth, he may find the Value of the Decimal Fraction by the former Part of this Article.

And, in the Fraction of a Foot, if the first Figure is under 5, reckon the two firft Figures as Half-Quarters of an Inch, abating 1, if they are above 13, or 2, if they are more than 38: But, if the first Figure fhould be above 5, fubtract 5 from it, and for the 5 reckon 6 Inches; then, to what remains of the firft Figure after the 5 is fubtracted, join the second Figure, and reckon thefe as Half-Quarters of an Inch; only, if they are above 13, abate 1, or, if above 38, abate 2, as in the Cafe of Farthings.

Thus, .12 of a Foot is 12 Half-Quarters of Inch, or
Inch and an Half,

1

.25 of a Foot is 24 Half-Quarters of an Ineh, or 3 Inches: For, from the 25 abating 1, there remains 24, which are Half-Quarters.

.45 of a Foot is 43 Half-Quarters of an Inch: For, from the 45 abating 2, there remains 43, which are HalfQuarters, that is, 5 Inches and 3 Half-Quarters.

.65 of a Foot is 7 Inches and 6 Half-Quarters: For, fubtracting 5 from the 6, there remains 1, to which joining the 5, it is 15: Now, for the 5 fubtracted reckon 6 Inches; then from the 15 abate 1, and the remaining 14 are Half-Quarters, or 1 Inch and 6 Half-Quarters; which, being added to the 6 Inches, makes 7 Inches and 6 HalfQuarters.

75 of a Foot is 9 Inches: For, fubtracting 5 from the 7, there remains 2, to which joining the 5, it makes 25: Now for the 5 fubtracted reckon 6 Inches; then from the 25 abate 1, and the remaining 24 are Half-Quarters, or 3 Inches; which, being added to the 6 Inches, makes 9 Inches.

.94 of a Foot is 11 Inches and 2 Half-Quarters: For, fubtracting 5 from the 9, there remains 4, to which join the 4, and it is 44: Now for the 5 fubtracted, reckon 6 Inches; then from the 44 abate 2, and the remaining 42 are Half-Quarters, or 5 Inches and 2 Half-Quarters; which, being added to the 6 Inches, makes II Inches and 2 HalfQuarters or I Quarter.

The Reader may try the Accuracy of these Conclufions, by finding the Value of the Decimal Fraction, by the former Part of this Article. If the Fraction had confifted of three Places, and the third Figure was above 5, in fome Inftances the Value of fuch Fraction may be more accurately determined by taking the third Place of Fractions into Confideration.

Article 48. To reduce the Parts of Coin, Weights, Measures, &c. into Decimals.

Rule. Set down for a Dividend the given Parts, if they are of one Denomination, or, if they are of feveral, reduce them to the leaft Denomination; to this annex Cyphers, marked as Fractions; and then divide it by that Number which makes up the Integer, and is of the fame Denomination with the Dividend, by Art. 44; and the Quotient is the Decimal fought.

Exam. I.

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Exam. 1. This being only Shillings, I annex Cyphers, and then divide by 20, the Shillings in a Pound: The Quotient .85 is the Decimal fought.

Exam. 2. This being Shillings and Pence, they must first be reduced to Pence; to which annex Cyphers, and then divide by 240, the Pence in a Pound: The Quotient .3875 is the Decimal fought.

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Exam. 3. This being Pence and Farthings, it must be reduced to Farthings; then, after the Cyphers are annexed, divide by 960, the Farthings in a Pound.

Exam. 4. Reduce this to 15 Quarters of an Inch, and then divide by 48, the Quarters of an Inch in a Foot.

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Thefe Examples are done in the fame Manner: There being 240 Pennyweights in a Pound Troy, the fifth Example is divided by that Number; where, the Remainder being always the fame, the Quotient Figure would be 6, if the Divifion was continued: And, in the fixth Example, the 12 Drachms are divided by 256, the Number of Drachms in a Pound Avoirdupoize.

In the Parts of a Pound Sterling the Decimal may be found without Divifion, as follows, viz. in the Parts of a Pound, for every two Shillings put a 1 in the Tenth's Place next the Dot for one Shilling put a 5 in the fecond Place of Decimals; and for fix Pence put a 2 in the fecond Place and a 5 in the third Place of Decimals: As to any lefs Quantity, reduce it to Farthings, and place the Number of Farthings in the fecond and third Places of Decimals, if they are more than 10, otherwife in the third Place only, obferving to add I to them, if they are more than three Pence.

Exam. 1.

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