| 3·1 | = 1240, | ·00062 | = ·00096875 |
|---|---|---|---|
| ·0025 | ·64 |
EXERCISES.
Shew that
| 15·006 × 15·006 - ·004 × ·004 | = 15·002, |
|---|---|
| 15·01 |
and that
| ·01 × ·01 × ·01 + 2·9 × 2·9 × 2·9 | = 2·9 × 2·9 - 2·9 × ·01 + ·01 × ·01 |
|---|---|
| 2·91 |
What are
| 1 | , | 1 | , and | 365 | , |
|---|---|---|---|---|---|
| 3·14159 | 2·7182818 | ·18349 |
as far as 6 places of decimals?—Answer, ·318310, ·367879, and 1989·209221.
Calculate 10 terms of each of the following series, as far as 5 places of decimals.
| 1 | + | 1 | + | 1 | + | 1 | + | 1 | + &c. = | ·71824. |
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 2 × 3 | 2 × 3 × 4 | 2 × 3 × 4 × 5 |
| 1 | + | 1 | + | 1 | + | 1 | + | 1 | + &c. = | 2·92895. | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | ||||||||
| 80 | + | 81 | + | 82 | + | 83 | + | 84 | + &c. = | 9·88286. | |
| 81 | 82 | 83 | 84 | 85 |
- We now enter upon methods by which unnecessary trouble is saved in the computation of decimal quantities. And first, suppose a number of miles has been measured, and found to be 17·846217 miles. If you were asked how many miles there are in this distance, and a rough answer were required which should give miles only, and not parts of miles, you would probably say 17. But this, though the number of whole miles contained in the distance, is not the nearest number of miles; for, since the distance is more than 17 miles and 8 tenths, and therefore more than 17 miles and a half, it is nearer the truth to say, it is 18 miles. This, though too great, is not so much too great as the other was too little, and the error is