Texas Instruments TI Programmable 57 User Manual

APPENDIX
D:
DISPLAYED.
RESULTS
VS
ACCURACY
The
basic
mathematical
tolerance
of
the
calculator
is
controlled
by
the
number
of
digits
it
uses
for
calculations.
The
calculator
appears
to
use
8
digits
as
shown
by
the
display,
but
actually
uses
11
digits
to
perform
all
calculations.
Combined
with
the
built-in
5/4
rounding
capability,
these
extra
digits
guard
the
8-digit
display
to
improve
accuracy.
Consider
the
following
example
in
the
absence
of
these
guard
digits.
x 3 = 99999999 (inaccurate)
The
example
shows
that]
—
3
=
.33333333
when
multiplied
by
3
produces
an
inaccurate
answer.
However,
an
eleven-digit
string
of
nines
will
round
to
|
when
rounded
to
8
places.
The
higher
order
mathematical
functions
use
interative
calculations.
The
cumulative
rounding
error
is
usually
maintained
below
the
8-digit
display
so
that
no
effect
can
be
seen.
The
three
“guard
digits”
act
to
protect
the
display
from
small
cumulative
errors.
Normally,
there
is
no
need
to
even
consider
these
guard
digits
In.certain
calculations,
however,
the
guard
digits
may
appear
as
an
answer
when
not
expected,
Results
of
two
computations
may
appear
to
be
equal
when
shown
in
the
display,
but
have
an
inequality
in
their
guard
digits.
If
these
two
results
are
subtracted,
the
calculator
may
display
a
nonzero
result
This
fact
is
especially
important
when
writing
your
own
programs
If
you're
testing
a
calculated
result
to
be
equal
to
another
value,
such
as
with
the
2nd)
EZ
instruction,
you
may
need
to
take
precautions
to
prevent
improper
evaluation
due
to
the
guard
digit
differences:
The
key
sequence
(EE)
[NV] (EE)
will
truncate
the
guard
digits
of
a
result
leaving
only
the
rounded
display
value
for
further
use.
For
the
standard
display,
results
are
accurate
for
all
calculations
that
do
not
violate
the
restrictions
listed
in
Appendix
C,
except
as
defined
below.
TRIGONOMETRIC FUNCTIONS
All
displayed
digits
are
accurate
for
a
+
36,000
degree
range
(+2007
radiansand
+40,000
grads).
Imgeneral,
the
accuracy
decreases
one
digit
for
each
decade
outside
this
specified
accuracy
range.
An
exception
is
the
tangent
of
an
odd
multiple
of
+90°,
t7/2
radians
or
+100
grads
that
results
in
an
overflow
condition
because
the
function
is
undefined
at
these
points.
Roots AND PowERs
There.can
be
some
accuracy
loss
for
roots
and
powers
in
‘calculations
when
the
base
(y)
gets
very
close
to]
and
the
power
(x)
gets
very
large
A-8

Texas Instruments TI Programmable 57 Specifications

General

Brand	Texas Instruments
Model	TI Programmable 57
Category	Calculator
Language	English