Re: TI-89: How to convert decimal sto fractions and vice versa
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Re: TI-89: How to convert decimal sto fractions and vice versa
> This isn't right. You don't need Partial Fractions to convert decimals to
> fractions, you just need to use the command exact(
>
> Just how would you use Partial Fractions to convert 45.328 (for example) to
> 5666/125, or onwards to 45 + 41/125 ?
>
> Dick
The information on exact() is useful here, because this is a _new_ function
in the TI-92 and TI-89 environment, and those moving up from TI-8x calcs
might not have noticed it. This will often give you a very satisfactory
conversion from a decimal expression to a fractional expression.
Not, however, in the case where there _is_ no terminating decimal
representation for the fraction being represented. For example, 5666/127
is 44.6141732283... No matter what decimal expression you feed to exact(),
you are not going to get 5666/127 as a result.
The method of partial fractions, in contrast, is perfectly general. It lets
you identify successive _convergents_ (better and better fractional
approximations) to a particular value. When the value you start with is
_close_ to the value of a particular fraction, you can easily notice this by
a large jump in the terms of the partial fraction at that point, and you
can overrule the remaining round-off error. Also, partial fractions can be
used on _any_ calculator with stored variables (even an old TI-81).
The idea of partial fractions is rather simple. For a given value X you
want to approximate with a fraction, you first identify (and hold in a
separate list) the _integer_ part of X. If X is the value 44.6141732283,
for example, your first term is 44. Now you subtract this term from X
(giving you the _fractional_ part of X) and take the _reciprocal_ of the
result. This will be a number greater than 1 (as an old math teacher, I
can't resist adding "why?"). In this case you would get 1.62820512821,
which becomes the new value of X. You repeat the process as many times as
you wish. If you are working with an approximate representation of a
fraction with a reasonably small-sized denominator, you will soon encounter
a reciprocal that is very close to an exact integer. Call it this integer,
and stop!
Then all you have to is build the actual fraction back together. In this
case, for example you have 44 + 1/ (1 + something). You build it back from
the bottom up. Of course you would want to write simple programs to help
you with this sort of thing. It's a nice process.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<
denominator