and so on, until no figures are left. Since we know from the beginning in what place the first figure of the quotient is, and also how many decimals are required, we can tell from the beginning how many figures there will be in the whole quotient. If the divisor contain more figures than the quotient, it will be unnecessary to use them: and they may be rejected, the rest being corrected as in (151): if there be ciphers at the beginning of the divisor, if it be, for example,
| ·003178, since this is | ·3178 | , |
|---|---|---|
| 100 |
divide by ·3178 in the usual way, and afterwards multiply the quotient by 100, or remove the decimal point two places to the right. If, therefore, six decimals be required, eight places must be taken in dividing by ·3178, for an obvious reason. In finding the last figure of the quotient, the nearest should be taken, as in the second of the subjoined examples.
| Places required, | 2 | 8 | |
|---|---|---|---|
| Divisor, | ·41432 | 3·1415927 | |
| Dividend, | 673·1489 | 2·71828180 | |
| 41432 | 2·51327416 | ||
| 258828 | 20500764 | ||
| 248592 | 18849556 | ||
| 10237 | [21] | 1651208 | |
| 8286 | 1570796 | ||
| 1951 | 80412 | ||
| 1657 | 62832 | ||
| 294 | 17580 | ||
| 290 | 15708 | ||
| 4 | 1872 | ||
| 4 | 1571 | ||
| 0 | 301 | ||
| 283 | |||
| 18 | |||
| 19 | |||
| Quotient, | 1624·71 | ·86525596 |
Examples may be obtained from (143) and (150).