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

17

7. How many repeating and how many non-repeating figures will
there be in the decimal equivalent to the fraction '-1-/2?
8. IWhat must be forms of the numerator and denominator, that
a fraction and its reciprocal may both be reducible to finite or repeating decimals?
9. If the number of figures in a recurring period of a decimal b s
one less than the denominator of the fraction, the sum of the figures
in the period - x number of figures. Give an example.
10. In every pure repeating decimal of an even number of repeating figures, the number composing the last half of the repeating
period is less by unity than the arithmetic complement of the first
half of the period. Exemplify this in reducing I to a decimal.
11. In the reduction of a fraction to a pure repeating decimal
having an even number of repeating figures, if the several remainders
arising from the reduction of the fraction be arranged equally in two
iseries, the sum of every two corresponding remainders will be equal
to the denominator of the fraction. Exemplify this by reducing -,- to
a decimal.
CONCRETE DECIMAILS.
XV.
1. Find the values of 1-0625 guineas; -83229 of ~1; '0425 of
~100; and -35687 of a moidore.
2. Find the exact value of -7365 of 6s. 8d.
3. Reduce *165625 of one guinea to the decimal of a pound; and
14526 of a pound to the decimal of a guinea.
4. Convert 8'775 shillings to the decimal of a moidore; and a-d.
to the decimal of a guinea.
5. Reduce 3s. dl. to the decimal of ~2 10s.; 3s. 11:-d. to the
decimal of a moidore; and 14s. 101d. to the decimal of ~1 4s. 3~d.
6. Reduce 2~,-. — to the fraction of a farthing, and find what decimal
of a farthing is one thousandth part of a pound.
7. Convert 3- of one penny to the decimal of half-a-crown; o of
one guinea to the decimal of one pound; 2- of 3s. 6d. to the decimal
of - of 6s. 8d.; - of 7 of one guinea to the decimal of ~5; andt
~2 12s. 6d. to the decimal of ~7 2s. 11-d.
8. Reduce ~2 12s. 6d. to the decimal of ~1, and conversely ~1 to
the decimal ~2 12s. 6d.
9. Find the value of -047460975 of ~10 13s. 4d., and -00390625 of
~20 10s. 6d.; and reverse the operations.
10. Reduce ~693 15s. to the decimal of ~750.
11. Explain the reason why any number of shillings may be
expressed in the decimal of a pound by multiplying the shillings by
5, and marking off two places of decimals.