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

16
83 and -0413: -297 and 12000: 412-421 and -002: '41716269841
and -0025:
~27, and '6: -0729 and '07: '142857 and '63: '285714 and 123:
~16 and -3: -9 and -7: -4925 and 75: -571428 and '0054:
*37 and -148: 1013 and -000132: 03428571 and -0025:
~5819 and 0159: '41716269841 and -12931: -5714285 and '63:
3-141 and 2-31: 13-2101 and 1 OOi: 7-00342 and '03:
101-50714285 and 11-63: 3-14 and 2-00637:
2'616, '00132, 1-0448 and '62639.
2. Shew that the product of two circulating decimals may produce
-a terminating decimal. Exemplify in the product of '2142857 by '46.
XIII.
1. Determine the quotients of the following decimals:~32 by 1'6, '16, '016, '0016, 160, 1600, and 16000 respectively
~72 by -3 '297 by -27: -6 by '9: -54 by -45: 1i42857 by -7:
~i42857 by 63: -63by 142857: -83 by.16:.0416 by '225: 013 by
-000132: -901 by-109:
25 2 by 25: 0025 by -025: 12-9769230 by -0857142:
~*47543 by 3-453: 1-956 by -836: 342753 by 2-57324.
2. Find the quotient arising from the product of 2 616 and '00132,
divided by the procuct of 1-0448 and 6-2639.
XIV.
1. Shew that when the fractions -7, 7, 7, -, - are reduced to
decimals, the periods of each will consist of the salle digits. What
explanation can be given?
2. In what sense can a finite fraction be said to be equal to an
Indefinite repeating decimal? How must the sign = be understood
in the expression -=3-' 353535.. adl infinitum, in order that the
expression may be satisfactory?
3. Shew that -03125= '03 = '031 '-o32 - '03125 - __
1 —'04 1 —'008 1-00' O 1G 1-0-' 0 O 32'
and '142857=- '14 -4 14 28 - '14285 - 142857 1
an ' 1- '02 1 — 0 1-o0004 1-'-00 00 1 —0 0000 0 7'
4. If the denominator of a fraction be prime to 3, the period of the
equivalent decilal is divisible by 9. Exemplify in —, -, 1.
5. Convert 1-449 to an ordinary fraction, and then convert the
fraction to a decimal, and explain the apparent discrepancy.
6. Find the first six decimal fractions of one, two, three, &c., places
of figures which approximate to the fraction -1 an, and shew that the
successive differences of the fraction and the decimals decrease.