The process of simply dropping extra digits is
called truncation. For example, when truncated to one
decimal place, both 1.834 and 1.8999978 become 1.8.
This process is also called “rounding down.”
See also
ERROR
;
FLOOR
/
CEILING
/
FRACTIONAL PART
FUNCTIONS
;
ROUND
-
OFF ERROR
.
round-off error (rounding error) The
ERROR
pro-
duced in
ROUNDING
a value to a prescribed number of
digits is called round-off error. For example, rounding
the quantity 6.42 to the nearest decimal place yields
6.4, introducing an error of 0.02.
Round-off errors typically amplify as one performs
calculations. For example, rounded to four decimal
places, cos 1°has value 0.9998. This suggests that
equals 5,000. This is false. The correct value
of this quantity is close to 6,565.8. As calculators
round all quantities to eight or 10 decimal places,
they too are susceptible to round-off errors and can
give erroneous results.
Royal Society (Royal Society of London) Founded
by royal charter granted by Charles II in 1660, the
Royal Society of London is the world’s oldest scientific
institution still in existence. Its mission today, as it was
at the time of its formation, is to disseminate current
knowledge about the natural world and to support and
promote continued scientific investigation.
Prior to the year 1600, scientists and scholars com-
municated results through the mail, as well as through
the publication of written texts following the invention
of the printing press in the 15th century. Such set and
rigid formats did not readily allow for the testing of
ideas and loose discussion of thought. In an attempt to
rectify this, in 1620 Francis Bacon (1561–1626) estab-
lished an organization called Novum Organum (The new
instrument) that provided a public forum for scientists,
and others, to meet, to discuss scientific ideas and find-
ings, and to learn of the general state of current scientific
thinking. Forty years later, the value of such an organiza-
tion was formally acknowledged, and the Royal Society
was formed. The eminent scientists of the day were
awarded membership to the society. S
IR
I
SAAC
N
EWTON
was president of the society from 1703 to 1727.
To be elected as a fellow of the Royal Society today
is deemed a truly prestigious honor. There are currently
65 Nobel laureates among the Society’s 1,300 fellows
and foreign members. Each member is given the right
to use the letters FRS (fellow Royal Society) after sign-
ing his or her name. The society maintains a Web site
(www.royalsoc.ac.uk).
The equally prestigious French Royal Academy of
Sciences was founded 6 years after the formation of the
Royal Society.
Russell, Bertrand Arthur William (1872–1970) Brit-
ish Foundations of mathematics, Philosophy Born on
May 18, 1872, in Ravenscroft, Wales, mathematical
logician and philosopher Bertrand Russell is remem-
bered for his text, cowritten with A
LFRED
N
ORTH
W
HITEHEAD
(1861–1947), Principia Mathematica (1910,
1
––––––
1 – cos(1)
452 round-off error
Bertrand Russell, an eminent mathematician of the 20th century,
was the first to discover a fundamental flaw in the elementary
theory of sets. (Photo courtesy of Topham/The Image Works)