This document introduces different types of numerical errors that can arise when using approximations to represent exact mathematical operations. It defines numerical error as the difference between the true value and approximation. The main type of error discussed is rounding off, which occurs when a large number is truncated to a usable number of figures. The document provides examples of numbers rounded off to four significant figures and references additional resources on the topic.

1. Presented by
Anil Pokhrel
Bsccsit
3 semester
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2. Introduction to error
 Numerical errors arise from the use of approximations
to represent exact mathematical operations:
TRUE VALUE = APPROXIMATION + ERROR
or,
ERROR (E) = TRUE VALUE ‐ APPROXIMATION
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4. DIFFERENT TYPES OF ERROR
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9. Rounding off:
 The error caused due to cut-off a large number
into usable number of figure is called round-off
error.
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10.  To round off a number to n-significant digits, discard
all digits to the right of the nth digit if this discarded
number is:
 - Exactly half a unit in the nth place, increase the nth
digit by unity if it is odd; otherwise leave it unchanged.
 Examples:
 Following numbers are rounded off to four
significant figures.
1.6583(1.658), 30.0567(30.06), 0.859378(0.8594),
3.14159(3.142)
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11. Reference
 https://en.wikibooks.org/wiki/Numerical_Methods/Er
rors_Introduction
 http://www.unistudyguides.com/wiki/Introduction_to
_Numerical_Methods
 Dr.B.S. Grewal -- Numerical Methods with programs
in C and C++
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