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

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6. Find the greatest common divisor of 36-595 and 57-980.
7. What is the least number which can be divided by each of the
numbers 1-36652 and 246-8642?
VII.
1. In what cases can an ordinary fraction be expressed by a finite
decimal? Shew that the number of decimal places in such cases may
be inferred from the factors of the denominator.
2. Of the fractions which produce terminating decimals, write
clown the denominators of such fractions as will produce decimals of
1, 2, 3, 4, 5, 6, 7 places respectively.
3. Convert the following fractions into decimals, and express in
words at length the values of the respective decimals:1 3 5 5 5 23 17 7 3476 C 98 372 323
2,, T TB, 8 C' 63 - 25? 0O? 1~o~6225 5 OO 8l722 TI2 25 0e0 T2 80U
And conversely, reduce the following decimals to ordinary fractions
in their lowest terms:~5, '75, '625, '3125, -15625, -0359375, -176, -000112, -318464,
'00341796875, 002176, '25234375.
4. Calculate the limits of the error made in taking -?i5 as an
approximate value of 3-1415926 to seven places of decimals.
VIII.
Calculate the following expressions, each to 7 places of decimals:80 81 82 83
1. +82l + + 83.84
1 1 1 1 1 I I 1_1
2. 1 - -+ F- 5 + +i- 7
3 5 7 9 11 13 15 17 19
1 1 1
3. 1 + 1.22+ 1.23.4+ 1.2.3.4.5.6.7.8.9
1 1 1 1 1 1I
4. I + -+ +~- $+- + 4. -
4 3 3. 32 3 35 36 -5 1 4 4.5 1 4.5.6 1 4.5.6.7 1
10 — 1 -2 1-+ 2.-3 1-.2.3.. 10+
cI + 1. 1-6 — 0i 284'1 ---'
6. 4f1 1 1 1
239 5 3 x 52 - + 5 x 5 7x5 + t9 59
IX.
1. What is meant by pure and by mixed circulating decimals?
Shew how to ascertain from knowing the factors of the denominators
of fractions, whether they produce pure or mixed circulating decimals. Is it indifferent whether the numerators are prime or composite numbers? Confirm the answer by examples.
2. Shew that in the reduction of a fraction to a decimal, if the
figures of the decimal do not terminate, they must recur in periods of
one, two, three, four, &c., figures, which are always less in number
than the denominator.