<s>
The	O
approximation	B-Algorithm
error	I-Algorithm
in	O
a	O
data	O
value	O
is	O
the	O
discrepancy	O
between	O
an	O
exact	O
value	O
and	O
some	O
approximation	O
to	O
it	O
.	O
</s>
<s>
This	O
error	O
can	O
be	O
expressed	O
as	O
an	O
absolute	B-Algorithm
error	I-Algorithm
(	O
the	O
numerical	O
amount	O
of	O
the	O
discrepancy	O
)	O
or	O
as	O
a	O
relative	B-Algorithm
error	I-Algorithm
(	O
the	O
absolute	B-Algorithm
error	I-Algorithm
divided	O
by	O
the	O
data	O
value	O
)	O
.	O
</s>
<s>
An	O
approximation	B-Algorithm
error	I-Algorithm
can	O
occur	O
for	O
a	O
variety	O
of	O
reasons	O
,	O
among	O
them	O
a	O
computing	O
machine	B-Algorithm
precision	I-Algorithm
or	O
measurement	O
error	O
(	O
e.g.	O
</s>
<s>
In	O
the	O
mathematical	O
field	O
of	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
the	O
numerical	B-Algorithm
stability	I-Algorithm
of	O
an	O
algorithm	O
indicates	O
how	O
an	O
error	O
occurring	O
in	O
one	O
of	O
the	O
algorithm	O
's	O
early	O
steps	O
effects	O
errors	O
in	O
other	O
parts	O
of	O
the	O
algorithm	O
.	O
</s>
<s>
An	O
error	B-Algorithm
bound	I-Algorithm
is	O
an	O
upper	O
limit	O
on	O
the	O
relative	O
or	O
absolute	O
size	O
of	O
an	O
approximation	B-Algorithm
error	I-Algorithm
.	O
</s>
<s>
As	O
an	O
example	O
,	O
if	O
the	O
exact	O
value	O
is	O
50	O
and	O
the	O
approximation	O
is	O
49.9	O
,	O
then	O
the	O
absolute	B-Algorithm
error	I-Algorithm
is	O
0.1	O
and	O
the	O
relative	B-Algorithm
error	I-Algorithm
is	O
0.1/50	O
=	O
0.002	O
=	O
0.2	O
%	O
.	O
</s>
<s>
The	O
correct	O
reading	O
being	O
6mL	O
,	O
this	O
means	O
the	O
percent	B-Algorithm
error	I-Algorithm
in	O
that	O
particular	O
situation	O
is	O
,	O
rounded	O
,	O
16.7	O
%	O
.	O
</s>
<s>
The	O
relative	B-Algorithm
error	I-Algorithm
is	O
often	O
used	O
to	O
compare	O
approximations	O
of	O
numbers	O
of	O
widely	O
differing	O
size	O
;	O
for	O
example	O
,	O
approximating	O
the	O
number	O
1,000	O
with	O
an	O
absolute	B-Algorithm
error	I-Algorithm
of	O
3	O
is	O
,	O
in	O
most	O
applications	O
,	O
much	O
worse	O
than	O
approximating	O
the	O
number	O
1,000,000	O
with	O
an	O
absolute	B-Algorithm
error	I-Algorithm
of	O
3	O
;	O
in	O
the	O
first	O
case	O
the	O
relative	B-Algorithm
error	I-Algorithm
is	O
0.003	O
while	O
in	O
the	O
second	O
it	O
is	O
only0.000003	O
.	O
</s>
<s>
There	O
are	O
two	O
features	O
of	O
relative	B-Algorithm
error	I-Algorithm
that	O
should	O
be	O
kept	O
in	O
mind	O
.	O
</s>
<s>
First	O
,	O
relative	B-Algorithm
error	I-Algorithm
is	O
undefined	O
when	O
the	O
true	O
value	O
is	O
zero	O
as	O
it	O
appears	O
in	O
the	O
denominator	O
(	O
see	O
below	O
)	O
.	O
</s>
<s>
Second	O
,	O
relative	B-Algorithm
error	I-Algorithm
only	O
makes	O
sense	O
when	O
measured	O
on	O
a	O
ratio	O
scale	O
,	O
(	O
i.e.	O
</s>
<s>
For	O
example	O
,	O
when	O
an	O
absolute	B-Algorithm
error	I-Algorithm
in	O
a	O
temperature	O
measurement	O
given	O
in	O
Celsius	O
scale	O
is	O
1°C	O
,	O
and	O
the	O
true	O
value	O
is	O
2°C	O
,	O
the	O
relative	B-Algorithm
error	I-Algorithm
is	O
0.5	O
.	O
</s>
<s>
But	O
if	O
the	O
exact	O
same	O
approximation	O
is	O
made	O
with	O
the	O
Kelvin	O
scale	O
,	O
a	O
1K	O
absolute	B-Algorithm
error	I-Algorithm
with	O
the	O
same	O
true	O
value	O
of	O
275.15K	O
=	O
2	O
°C	O
gives	O
a	O
relative	B-Algorithm
error	I-Algorithm
of	O
3.63	O
.	O
</s>
<s>
The	O
limits	O
of	O
these	O
deviations	O
from	O
the	O
specified	O
values	O
are	O
known	O
as	O
limiting	B-Algorithm
errors	I-Algorithm
or	O
guarantee	O
errors	O
.	O
</s>
