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. Two shillings is £·100 | One shilling is £·050 | Sixpence is £·025 | One farthing is £·001 | 04⅙ 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._ Thus, 0_s._ 3½_d._ = £·014 0_s._ 7¾_d._ = £·032 1_s._ 2½_d._ = £·060 1_s._ 11¼_d._ = £·096 2_s._ 6_d._ = £·125 2_s._ 9½_d._ = £·139 3_s._ 2¾_d._ = £·161 13_s._ 10¾_d._ = £·694 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 farthing[59] above the last sixpence, and an additional 1 for every six farthings, or three halfpence._ [59] The student should remember all the multiples of 4 up to 4 × 25, or 100. 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 The figures of ¹/₆ are 166666... ” ²/₆ ... 333333... ” ³/₆ ... 5 ” ⁴/₆ ... 666666... ” ⁵/₆ ... 833333... 0_s._ 3½_d._ = ·014|58|3333... 0_s._ 7¾_d._ = ·032|29|1666... 1_s._ 2½_d._ = ·060|41|6666... 1_s._ 11¼_d._ = ·096|87|5 2_s._ 6_d._ = ·125|00|0000... 2_s._ 9½_d._ = ·139|58|3333... 3_s._ 2¾_d._ = ·161|45|83333... 13_s._ 10¾_d._ = ·694|79|1666... The following examples will shew the use of this rule, if the student will also work them in the common way.