APPENDIX VI. ON DECIMAL MONEY.

Of all the simplifications of commercial arithmetic, none is comparable to that of expressing shillings, pence, and farthings as decimals of a pound. The rules are thereby put almost upon as good a footing as if the country possessed the advantage of a real decimal coinage.

Any fraction of a pound sterling may be decimalised by rules which can be made to give the result at once.

Thus, every pair of shillings is a unit in the first decimal place; an odd shilling is a 50 in the second and third places; a farthing is so nearly the thousandth part of a pound, that to say one farthing is ·001, two farthings is ·002, &c., is so near the truth that it makes no error in the first three decimals till we arrive at sixpence, and then 24 farthings is exactly ·025 or 25 thousandths. But 25 farthings is ·026, 26 farthings is ·027, &c. Hence the rule for the first three places is

One in the first for every pair of shillings; 50 in the second and third for the odd shilling, if any; and 1 for every farthing additional, with 1 extra for sixpence.

In the fourth and fifth places, and those which follow, it is obvious that we have no produce from any farthings except those above sixpence. For at every sixpence, ·00004⅙ is converted into ·001, and this has been already accounted for. Consequently, to fill up the fourth and fifth places,

Take 4 for every farthing¹ above the last sixpence, and an additional 1 for every six farthings, or three halfpence.

The remaining places arise altogether from ·00000⅙ for every farthing above the last three halfpence; for at every three halfpence complete, ·00000⅙ is converted into ·00001, and has been already accounted for. Consequently, to fill up all the places after the fifth,

Let the number of farthings above the last three halfpence be a numerator, 6 a denominator, and annex the figures of the corresponding decimal fraction.

It may be easily remembered that