<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
and	O
scientific	O
computing	O
,	O
truncation	B-Algorithm
error	I-Algorithm
is	O
an	O
error	O
caused	O
by	O
approximating	O
a	O
mathematical	O
process	O
.	O
</s>
<s>
Given	O
the	O
following	O
infinite	O
series	O
,	O
find	O
the	O
truncation	B-Algorithm
error	I-Algorithm
for	O
if	O
only	O
the	O
first	O
three	O
terms	O
of	O
the	O
series	O
are	O
used	O
.	O
</s>
<s>
However	O
,	O
if	O
we	O
are	O
calculating	O
the	O
derivative	O
numerically	B-General_Concept
,	O
has	O
to	O
be	O
finite	O
.	O
</s>
<s>
The	O
error	O
caused	O
by	O
choosing	O
to	O
be	O
finite	O
is	O
a	O
truncation	B-Algorithm
error	I-Algorithm
in	O
the	O
mathematical	O
process	O
of	O
differentiation	O
.	O
</s>
<s>
However	O
,	O
if	O
we	O
are	O
calculating	O
the	O
integral	O
numerically	B-General_Concept
,	O
we	O
can	O
only	O
use	O
a	O
finite	O
number	O
of	O
rectangles	O
.	O
</s>
<s>
The	O
error	O
caused	O
by	O
choosing	O
a	O
finite	O
number	O
of	O
rectangles	O
as	O
opposed	O
to	O
an	O
infinite	O
number	O
of	O
them	O
is	O
a	O
truncation	B-Algorithm
error	I-Algorithm
in	O
the	O
mathematical	O
process	O
of	O
integration	O
.	O
</s>
<s>
find	O
the	O
truncation	B-Algorithm
error	I-Algorithm
if	O
a	O
two-segment	O
left-hand	O
Riemann	O
sum	O
is	O
used	O
with	O
equal	O
width	O
of	O
segments	O
.	O
</s>
<s>
Occasionally	O
,	O
by	O
mistake	O
,	O
round-off	B-Algorithm
error	I-Algorithm
(	O
the	O
consequence	O
of	O
using	O
finite	O
precision	O
floating	B-Algorithm
point	I-Algorithm
numbers	I-Algorithm
on	O
computers	O
)	O
,	O
is	O
also	O
called	O
truncation	B-Algorithm
error	I-Algorithm
,	O
especially	O
if	O
the	O
number	O
is	O
rounded	O
by	O
chopping	O
.	O
</s>
<s>
That	O
is	O
not	O
the	O
correct	O
use	O
of	O
"	O
truncation	B-Algorithm
error	I-Algorithm
"	O
;	O
however	O
calling	O
it	O
truncating	O
a	O
number	O
may	O
be	O
acceptable	O
.	O
</s>
<s>
Truncation	B-Algorithm
error	I-Algorithm
can	O
cause	O
within	O
a	O
computer	O
when	O
because	O
(	O
like	O
it	O
should	O
)	O
,	O
while	O
.	O
</s>
<s>
Here	O
,	O
has	O
a	O
truncation	B-Algorithm
error	I-Algorithm
equal	O
to	O
1	O
.	O
</s>
<s>
This	O
truncation	B-Algorithm
error	I-Algorithm
occurs	O
because	O
computers	O
do	O
not	O
store	O
the	O
least	O
significant	O
digits	O
of	O
an	O
extremely	O
large	O
integer	O
.	O
</s>
