JB/135/080/002

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Decimal Fractions

To reduce a Vulgar
Fraction into a decimal

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

If after you have
made use of all the
Cyphers annexed to the
numerator there is a
remainder annex Cyphers
thereto and continue your
division till it divide off
or arrive to what degree
of exactness you think
proper.-

Always observe to
set a point betwixt the
numerator and the Cyphers
annexed thereto and that
the quotient have as
many places as you annex
Cyphers to the numerator
and remainders; and if
it be deficient let the
want be supplied by prefixing
as many Cyphers
to the quotient as it falls
short.-

Those decimals
that are reduced from
such a Vulgar Fraction
whose numerator with
Cyphers annexed is an
aliquot part of or can
be measured by its denominator
are finite or
determinate decimals.-
as No fraction will
produce a finite decimal
but such whose denominator
is 2 or 5 and
their multiples.-

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But such as are produced from a Vulgar fraction whose numerator with cyphers annexed is no aliquot part of or cannot be measured by its denominator will be indeterminate or endless.- In circulating decimals if one figure only repeats it is called a single repetend.- To avoid the trouble of writing down unnecessary figures a single repetend is denoted by the repeating digit dashed. The decimals in which two or more figures circulate are called compound repetends & the manner of distinguishing them is by dashing the first and last figure of the repetend by which means we make one place of the repetend sufficient.- To reduce Coin Weights Measures &c into decimals. Reduce the different species into one viz the lowest denomination they consist of for a divident then reduce the integer into the same denomination for a divisor; the result will be the decimal required.- Write the given denominations or parts orderly under each other the inferior or least parts being uppermost let these be the dividends.-

Against each part on
the left hand write the
number thereof contained
in one of its superior
let these be the divisors.

The begininning
with the upper one write
the quotient of each division
as decimal parts on the
right hand of the dividend
next below it, and let
this mixed number be
divided by its divisor &c
till all be finished and
the last quotient will be
the decimal sought. —

The decimal may
be readily found by the
rule of practice namely
by considering the next
inferior denomination as
aliquot parts of the integer
and those still lower as
aliquot parts of the superior
ones or of each other
the Sum of all those
aliquot parts will be the
decimal required. —

To reduce any decimal
into the equivalent
known parts of Coin Weight
or Measure -

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

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Identifier: | JB/135/080/002"JB/" can not be assigned to a declared number type with value 135.
Date_1		Marginal Summary Numbering
Box	135	Main Headings
Folio number	080	Info in main headings field	decimal fractions
Image	002	Titles
Category	private material	Number of Pages	2
Recto/Verso	recto	Page Numbering
Penner	sir samuel bentham	Watermarks	1798
Marginals		Paper Producer
Corrections		Paper Produced in Year	1798
Notes public		ID Number	46198
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