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.
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... |
| 0s. | 3½d. = | ·014 | 58 | 3333... |
| 0s. | 7¾d. = | ·032 | 29 | 1666... |
| 1s. | 2½d. = | ·060 | 41 | 6666... |
| 1s. | 11¼d. = | ·096 | 87 | 83333... |
| 2s. | 6d. = | ·125 | 00 | 0000... |
| 2s. | 9½d. = | ·139 | 58 | 3333... |
| 3s. | 2¾d. = | ·161 | 45 | 83333... |
| 13s. | 10¾d. = | 694 | 79 | 1666... |
The following examples will shew the use of this rule, if the student will also work them in the common way.
To turn pounds, &c., into farthings: Multiply the pounds by 960, or by 1000-40, or by 1000(1-⁴/₁₀₀); that is, from 1000 times the pounds subtract 4 per cent of itself. Thus, required the number of farthings in £1663. 11. 9¾.
| 1663·590625 × 1000 | = | 1663590·625 |
| 4 per cent of this, | 66543·625 | |
| No. of farthings required, | 1597047 |