Elementary arithmetic, with brief notices of its history... by Robert Potts.

26

RESULTS, HINTS, ETC., FOR THE EXERCISES.
ABSTRACT DECIMALS.
I.
1. Art. 1. 2. 321'123=300+20+1+-+ T - +, which expressed in words
is three hundred and twenty-one, together with one-tenth, two-hundredths, and
three-thousandths. 3. Art. 2. 5. Art. 4, note, p. 3.
II.
(1) 725'2251. (2) 21-2534. (3) 13874-763903.
(4) 106-32275. (5) -0095.
2. The following are the decimals which can be formed with the four figures:
'0379 '3079 '7039 '9037
'0397 '3097 '7093 '9073
'0739 '3709 '7390 '9307
'0793 '3790 '7309 '9370
~0973 '3970 '7930 '9730
~0937 '3907 '7903 91703
The sum of these decimals is 12'6654.
III.
The following are the differences of the decimals:
-018: '001: 096: 17-28659: 179973: 233'90001: '099: 785-999307
'00732421375.
IV.
1. Art. 6. 3. 9-25: '2: 15: '842: 1000: '1: 7586425: 15'525: 1'5 625:
'00003738028: '000001: 82-75139486: 33'57845799: '000365625: 56-173002:
~0000000289536. 4. 2 2939153468.
V.
1. 1: '3: '003: '005: '00011: -000000001: '0079: 1-25: '06: '005: 170 01:
18-45: 10'003.
2. 2: 12: 525: 37: 46: 618: 873: 151.
3. 40: 3680: 400000: 5000: 70: 17750000: 605000000: 1600.
4. '0005 and 2000: 1000000 and '000001: 2-5 and '4: -4 and 2-5: 4 and 2'5.
5. Art. 8. 6. Art. 7. The value of the remainder is estimated after the division
from the decimal point in the dividend to the last figure used in the division.
7. The quotient of the first example is 20495'1856946, and the value of the
remainder is '000000000258. 8. 1'002... 9. '01. 10. 499'998. 11. 14'9816.
12. '0000005.
VI.
1. If '625625 be a divisor, the equivalent multiplier is -G1 or I. 2. The multiplier is 15625. 3. 625. 4. 263 times, with a remainder '0027, which is one-third(
of '0087. 5. 3'97 is the quotient, and '00035 is the remainder. 6. '65. 7. Tihe
least common multiple.
VII.
1. Art. 10. 2. Art. 10. 4. '.=3'1415964, the error is -0000038.
VIII.
1. 3-9515026. 2. '7604602. 3. 1-7177815. 4. -4993585.
5. '00000000096098035. 6. '0031209.