_First._ The divisor, since it ends in 5, must be multiplied by 2,
giving 730. Dropping the O, we have 73 for the prepared divisor.
_Second._ The last figure of the prepared divisor being 3, this is the
extraneous multiplier. Multiplying the truncated divisor, 7, by the
extraneous multiplier, 3, and adding 1, we have 22 for the current
multiplier.
_Third._ The dividend, 1883, has now to be multiplied by the product
of 3, the extraneous multiplier, and 2, the multiplier used in
preparing the divisor. The product, 11298, is the prepared dividend.
_Fourth._ From the prepared dividend, 11298, we cut off the last
figure 8, and multiply this by the current multiplier, 22. The
product, 176, is added to the truncated dividend, 1129, and gives 1305
for the first modified divisor. The whole operation is shown thus:
1 8 8 3
6
-------
1 1 2 9|8
1 7 6 -
-----
1 3 0|5
1 1 0 -
-----
2|4 0
8 8 ---
---
|9 0
-----
1 9|8
1 7 6 -
-----
1 9|5
1 1 0 -
-----
1 2|9
1 9 8 -
-----
2|1 0
2 2 ---
2 4
We stop at this point because 24 was a previous modified dividend,
written under the form 240 above. Our two infinite numbers (which need
not in practice be written down) are, with their difference:
. .
10,958,904,058 . .
10,958,904,109.5890410958904
----------------------------
. .
51.5890410958904
. .
Hence the quotient sought is 5.158904109.
_Example 2._ Find the reciprocal of 333667.
The whole work is here given:
3 3 3 6 6|7 |7
2 3 3 5 6 7 - 1 6 3 4 9 6|9
2 1 0 2 1 0 3 -
-------------
2 2 6 5 5 9|9
2 1 0 2 1 0 3 -
-------------
2 3 2 8 6 6|2
4 6 7 1 3 4 -
-----------
7 0 0 0 0 0
. .
_Answer_, 0.000002997.
_Example 3._ Find the reciprocal of 41.
_Solution._--
4|1 |9
----- -----
3 7|9 3 3|3
- 1 1 1 -
-----
1 4|4
1 4 8 -
-----
1 6|2
7 4 -
---
9 0
. .
_Answer_, 0.02439.