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152
Rule.
In multiplying, observe
to add to the
right hand place of
the product, so many
units as there are tens
in the product of the
left hand place of the
repetend; and the product
shall contain a
repetend, whose places
are equal to those in
the multiplicand; &
if there are more
places of figures in
the multiplier than
one, make all the
several products conterminous
towards
the right hand.
Case VII.
If the multiplier be a
compound repetend,
Rule.
Multiply each figure
of the repetend, and
add the several products
together; then
add the result in this
manner; set the left
hand figure so many
places forward
as exceeds the number<b/>
of places in the
repetend by one, and
the rest of the figures
in order after it; &
thus proceed, till the
result last added be
carried beyond the
first; lastly, add the
several results together,
beginning under
the right hand
place of the first; &
from thence dash as
many figures for a
repetend, as the repetend
of the multiplier
consists of.
If the multiplier
hath any terminate
places joined with
the repetend, and if
the repetend be small,
and these many, multiply
and add the products
of the repetend
first; then multiply
by the terminate figures,
and add their
products to the sum
of the products of
the
the repetend; and to
this last result, add
the said sum of the
repetend products.
But if the terminate
figures are few, and
the places of the repetend
many, subtract
the terminate figures
from those of the repetend,
and multiply
by the remainder as
a repetend.
Case VIII.
If both factors have
compound repetends,
Rule.
Proceed as in the two
last cases.
Division of Decimals.
Case. I.
When the divisor and
dividend are both
finite decimals,
Rule.
Divide as in whole
numbers, and from
the right hand of the
quotient point off for
decimals so many
places as the decimal
places in the dividend
exceed those in the divisor;
and those to the
left, if any, are integers,
but if the places of the
quotient are not so
many as this rule
requires, supply the
defect by prefixing cyphers
to the quotient;
but if the decimal
places in the divisor
be more than those
in the dividend, annex
cyphers to the
dividend to make
them equal, and the
quotient
will be integers
untill all those
cyphers are used
Case II.
To contract the work
of division, when the
divisor consists of many
decimal places.
Rule.
Having determined
the value of the quotient
figures, let each
remainder be a new
dividend
dividend; and for every
such dividend, point
off one figure from the
right hand of the divisor;
observing at
each multiplication to
have regard to the increase
of the figure so
cut off, as in contracted
multiplication.
Case III.
If the dividend be a single repetend.
Rule.
If it be a single repetend,
bring down the
circulating figure untill
the quotient either repeats,
or is as exact as
required; but if the
repetend in the dividend
be a compound
one, then bring down the
circulating figures in
the same order they
stand in; and when
you have got through
them all, bring down
the first figure in the
repetend over again;
and so proceed untill
your quotient either
repeats, or becomes as
exact as is necessary
Case IV.
If the divisor be a
single prepetend,
Rule.
place the dividend under
itself, but one place
forward towards the
right hand, which subtract
from the dividend;
the remainder will be
a new dividend, which
divide by the divisor,
in the same manner
as if it was a terminate
number. But if the
divisor consists of terminate
numbers,
joined to the repetend,
subtract those terminate
numbers from the
divisor, and subtract
the dividend as before
directed, and the remainder
will be a new
divisor & dividend.
Case. V.
If a compound repetend
is found in
your divisor only, or
in
in both your divisor
& dividend,
Rule.
Set the divisor and
dividend under themselves,
each so many
places towards the right
hand, as there are places
in the reprehend
of the divisor; which
subtract as in the last
case, and the remainder
will be a new divisor
& dividend. But
if the divisor is a compound
reprehend
without any terminate
figure, divide by it as
a terminate
number;
first subtracting the
dividend from itself,
as before directed.
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Identifier: | JB/135/088/003 "JB/" can not be assigned to a declared number type with value 135.
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003 |
reduction of decimals / addition of decimals / subtraction of decimals / division of decimals |
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collectanea |
4 |
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