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

15
3. Change the following fractions into their equivalent decimals: —
1 4 5 4 11 1 5 15 8
t -7-1 - TTY T,' TT 17 3-71 T- 53'
And conversely, reduce the following pure repeating decimals to
their equivalent fractions in the lowest terms:3, -571428, 45, 45, 846153, *0588235294117647, i35, -36585,
1509433962264.
4. Reduce the following fractions to decimals:1 11 1 19 71 11 189 1 5359
T, 1~2 T T8 171 T- 2-U IT 926-7 Tv9-989 198000'
And conversely, convert the following mixed repealing decimals into
equivalent fractions in the lowest terms:1 6,.916,.02083, 10714285,.6761904,.5238095,.20432, -0O05,
-027065.
5. Shew that -I.= '03448-; hence, without any further division,
find the value of 2- to ten places of decimals.
X.
1. In the addition and subtraction of two or more repeating
decimals, how may the number of repeating figures in the sum or
difference be ascertained? How many repeating decimals will be in
the sum and difference of two decimals, one of which contains four,
and the other six repeating figures?
2. Find the sums of the following repeating decimals:12-16, 110-354 and 1-1412: 3,.123 and -5678
6-27, 18-561, 12-345 and 1-0001: 1-03, 2'003 and 3-0003:
10-16, 300-857142, 3-95238, -073224, and 1-01i85646:
257-3061, 5-6819, -1867312 and -153598:
10-12473, 62-91, 400-0003 and -2564:
1-5, 4-023, 12-845 and -2420329:
100-0017, 2-38457789, 109-200471385 and 3.456.
3. Shew that nine times the sum of -73 and *37 is an integer.
XI.
1. Find the differences of the following repeating decimals, and
express the results as fractions in their lowest terms.
3-27 and 4-16: -6 and -296: -734625 and '307196: '6123 and '0416:
*3639 and 1-02371280: -089285714 and -09: 14-2578 and 3-145.
-34027 and -127: -123 and -1234: -01934 and -273242.
2. Reduce -265625 and 714285 to fractions, and find their difference.
XII.
1. Find the products of the following decimals: