Representation of numbers.

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Representation of numbers
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Representation of numbers.

• Significant digits of a number
• The significant digits of a number are those
  that can be used with confidence for
  calculations. They correspond to the number of
  certain digits plus one estimated digit.
• The number of significant digits of a number is
  equal to the no. Of digits present from first non
  zero digit to last. (towards right).
• Example-
• 0.1,0.05,0.0009?one significant digit numbers.
• 1.2,0.023,0.000045,0.10?two significant digit
  numbers.
• 0.004856,0.00004200,0.01005?four significant
  digit numbers

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Scientific notations

• 4.53?104?Three significant digit number
• 4.530?103?Four significant digit number
• 4.5300?102?Five significant digit number.

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Floating point representation.

In decimal notation every real number is
represented by either finite or infinite sequence
of digits.
In floating point representation , the decimal
number x expressed as
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Example

Number
Floating point representation
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Normalized floating point representation

• The floating point number is said to be
  normalized, if d1?0 or d1d2d3..dn0.
• Example-
• 0.0294100?Non normalized floating point number.
• 0.29410-1?Normalized floating point number.

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Example

Normalized floating point number
Number
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Exercise

• Write the following numbers in normalized
  floating point form.
• 0.000527532, 12.003,-0.00436,23.2.

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Rules for Round-off a number to n significant
digits

To round-off a given decimal number up to n
significant digits we need to follow the
following rules
1) Discard all the digits right to nth digit of
given number
2) Add 1 to nth digit if (n1)th digit is greater
than 5.
3) Un alter nth digit if (n1)th digit is less
than 5.
4) Add 1 to nth digit if (n1) th digit equal to
5 and nth digit is odd.
5) Un alter nth digit if (n1)th digit is equal
to5 and nth digit is even.
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Example

Round-off the following numbers up to five
significant figures (digits).
Round-off Number
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Exercise

• Write the numbers 23.49,-302.867, 0.000527532 in
  floating point form rounded to 4 significant
  figures.

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Thank You ALL

• Presented by
• Boina Anil Kumar
• Asst.Prof in Mathematics
• MITS, Rayagada.
• Odisha, India
• E-mail anil.anisrav_at_gmail.com
• Visit at http//www.mits.edu.in/academics.phpfac
  ulty_BSH-tab