Education > Complete treatise on practical arithmetic and book-keeping

REDUCTION OF DECIMALS.
* I. To reduce a vulgar fraction to an equivalent decimal.
■ Rule.
Divide the numerator by the denominator as in division
decimals, and the quotient will be the decimal required.
Examples.
Reduce §•, 4> i» and to decimals.
Reduce 4 to a decimal.
Reduce tVt o a decimal.
Reduce to a decimal-
* Since to throw any vulgar fraction, whose denominator is a prime
umber, greater than what it is common to divide by in one line,
j to a decimal, consisting of a great number of figures, has enga-
;d the attention of many eminent persons, I shall here set down
| ie method which Mr. Colson has given in page 162 of Sir Isaac
ewton’s fluxions; which method performs the work much sooner
an any other that I know of.
■ The method will be best explained by an example^ thus: “ Suppose
|or instance) I would find the reciprocal of the pritne number 2‘9,
r the value of the fraction ^ in decimal numbers. I divide 1000©
r 29, in the common way, so far as to find two or three of the first
pires, or till the remainder becomes a single figure, and then I a$-
me the supplement to complete the quotient. Thus I shall have
?=0O3448t87 for the complete quotient; which 'equation, if 1
ultiply by the numerator 8, it will give ^=0-27J84«^ or rather
ys=0'27586-^. Isubstisute this instead of the fraction in the first
nation, and I shall have ^=0-0344827586^. Again, I multiply.
is equation by 6, and it will give/^ =0-2068965517^, and then by
rtitution-^=04)3448275862068965517^ Again, I multiply
equation by 7, and it becomes ^=0-24137931034482758620-
r,and then, by substitution, Ar=0-O3448275862O6896551734137-
1103448278620-1°, where every operation Will at least double the
mber of figures found by the preceding operation. And this
11 be an easy expedient for converting Division into Multiplication
all cases. For this reciprocal of the divisor being thus fotiad, it
iy be multiplied into the dividend to produce the quotient.”