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

27
IX.
1. Arts. 11 —14. 2. Art. 11. 5. Art. 10, note, p. 7.
X.
1. Art. 15. The L.C. M. of 4 and 6 is 12, which is the number of repeating
decimals in the sum and difference of two repeating decimals of four and six places
respectively.
2. 123-66242: 1-024313242132: 38-1848938847: 60369: 315-20412834333626:
263-32847303: 473.29i46340760202: 186: 215-043283428234.
3. 10.
XI.
1. 893=: 37 =-: -.27426 =-2.0: 5706 5=:.65974883:
-010714285: 11-112270: 21249: 0001911; -2538988.
2. T- i_=.
XII.
1. 372s: 356 4: 7 00o:. A s G 2 o25 reduce to lowest terms: 5: 5 __
1.TT: 52:a22l: 22f: B 5sF '- Y4 1 rv i 9r; rA: Ua4 -:T 4
4790494510919: 8 Ad-: '3: 1322027: 399. 1166 6 296 R241
2. The quotient is 1317 X132
- 5219 X2 X 2639
repeating decimal, as 1 a the limit of the value which the decimal can never exceed. It
may easily be shewn that the more figures of the decimal are taken, the larger the
decimal ecoes, and will continue to approach in actual value to the factio, but
within a difference less than can be assigned by any fraction whatever.
5. A. 1Ar6. 6 Art. 9, note 2, p. 6.
2. The quotient is 1317x132
5219 X 62639
XIV.. Any finite fraction having thonly be factor 7 in te denominator, is apparently one infinite
ill produce a repeating decimal, but when the actiodecimal can neveis reduced to its lowest term
may easily be shen thator consists of factore figures of the decimal are taen, the larger the
deimal becomes, and will continue to apprnd the denominator mst ctai one or moe faction, but
ihin a differen ce less than can be ssig by ay factio whatever10.
9 t.Take as an examplert. 9, note 2, 875142. The number of repeati ures is 6, and
the sum of the digits of the period is 27, and 27 =42X 6.
10. Heran hi the factor 7 in the denominaplemet of 154 is 1000-154846.apparently one which
ll is reduce a repeatinga decimal, but when the repeating figureduces in the decimal ae 22,
the denominator consists of factors each equal to 2. Art. 10.
8. Bothnd the first eleven and the second eleven remaust continders are respectivelydifent17, 9, 21, 3, 7, 1,Art. 10, 8, 11, 18, 19,
9. Take q as an example, q = '~7514I. The number of repeating figures is 6, and
10. Here =-'84615~' and the A. Complement of 154 is 1000- 154 = 846.
11. When.4 is reduced to a decimal, the repeating figures in the decimal are 22,
and the first eleven and the second eleven remainders are respectively —
17, 9, 21, 3, 7, 1, 10, 8, 11, 18, 19,
6, 14, 2, 20, 16, 22, 13, 15, 12, 5, 4.
CONCRETE DECIMALS.
XV.
1. ~1 2s. 3 d.: 16s. 7&d. -9984: ~4 5s.: ~4 16s. 41d. '0352. 2. 9s. 94d. -3.
3. One the reverse of the other. 4. '325 of 1 moidore, and '002976190i of one