JB/135/088/002

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Collectanea

Reductions of Decimals

Case 1

To reduce a vulgar
fraction into a decimal

Rule

Annex cyphers to
the numerator, till it
be equal to, or greater
than the denominator;
then divide by
the denominator,
and the quotient will
be the decimal sought.

Case II

To reduce coins,
weights, measures &c
into decimals

Rule

Reduce the different
species into one, viz:
the lowest denomination
they consist of
for a dividend; then
reduce the integer into
the same denomination
for a divisor;
the result will be the
decimal required.

Case III

To reduce any decimal
into the equivalent
known parts of coin,
weight, or measure

Rule

Multiply the given
number by the number
of units contained in
the next inferior
denomination, cutting
off as many figures
from the product as
the given decimal consists
of; then multiply
the remaining
parts (if any) by the
next lower denomination,
cutting off as
before; and thus
proceed till you have
converted your decimals,
or come to the
lowest part; and
the several figures
to the left hand of
the separating points
will be the several
parts of the quantity
required.

Case IV.

To reduce a decimal
into its least equivalent
vulgar fraction.

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1st. If the decimal be
finite.

Rule.

Under the given decimal<
lb/> write an unit, with as many cyphers as
the decimal consists of
places; then divide both
the numerator and denominator
by the
greatest common measure,
which gives the
least equivalent vulgar
fraction required.

2nd. If the given decimal
be a repetend,

Rule.

The decimal is the numerator
of a vulgar
fraction, whose denominator
consists of as
many nines as there
are recurring places
in the given decimal;
both which divide by
their greatest common
measure, and their
quotient will be the least
equivalent vulgar
fraction.

3rd When the given decimal is part final,
and part a circulate,

Rule.

To as many nines
as there are figures
in the repetend, annex
as many cyphers
as there are
finite places for a
denominator; then
multiply the nines
in the said denominator
by the finite
parts, and to the product
add the repeating
decimal for a numerator;
these divided by
their greatest common
measure, will give the
least equivalent fraction.

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Addition of Decimals.

Case. I.

To add finite decimals.

Rule.

Add as in whole
numbers, and from
the sum or difference,
cut off so many places
for decimals, as
are equal to the greatest
number of decimal
places in any
of the given numbers.

Case. II.

To add decimals
wherein are single
repetends.

Rule.

Make every line end
at the same place,
filling, up the vacancies
by the repeating
digits, and annexing
a cypher or cyphers
to the finite
terms; then add as
before, only increase
the sum of the right
hand row with as
many units as it
contains nines; and
the figure in the sum,
under that place,
will be a repetend.

Subtraction of
Decimals.

Case I.

To subtract finite
decimals.

Rule.

Having first set
down the greater of
the two numbers given,
set down the less
under it, then subtract
as in whole numbers.

Case. II.

To subtract decimals
that have repetends.

Rule.

Make the repetends
similar & conterminous,
and subtract
as in the last case:
observing only, if the
repetend of the number
to be subtracted,
be greater than the
repetend of the number
it is to be taken
from, then the right
hand figure of the
remainder must be
less by unity, than it
would be, if the expressions
were finite.

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Identifier: | JB/135/088/002"JB/" can not be assigned to a declared number type with value 135.
Date_1		Marginal Summary Numbering
Box	135	Main Headings	posology
Folio number	088	Info in main headings field	collectanea
Image	002	Titles	reduction of decimals / addition of decimals / subtraction of decimals / division of decimals
Category	collectanea	Number of Pages	4
Recto/Verso	recto	Page Numbering	[[page_numbering::f153 / / f152 [sic] /]]
Penner		Watermarks
Marginals		Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	46206
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