Transcript CPA4-ComputerError

ME 142
Engineering Computation I
Computer Precision
&
Round-Off Error
Numerical Error
 Two major forms of numerical error:


Round-off error
Truncation error
 Round-off Error

Is due to the fact that computers can represent only quantities with a
finite number of digits
 Truncation Error

Is introduced because numerical methods employ approximations to
represent exact mathematical operations and quantities
Significant Figures
 Significant digits of a number are those that can be used
with confidence
 Typically, 3 to 4 significant digits is common in the final
answer of engineering calculations


Keep all available significant figures on intermediate calculations
Round final answer to 3 or 4 significant digits
 Significant Figures in Excel

By default Excel keeps all available significant figures and displays
a round answer, per user setting
Accuracy vs. Precision
 Two terms commonly used within engineering

Both are important and necessary
 Accuracy refers to how closely a computed or measured
value agrees with the true value.
 Precision refers to how closely individual computed or
measured values agree with each other.
Increasing Precision
Increasing Accuracy
Inaccurate & Imprecise
Accurate & Imprecise
Inaccurate & Precise
Accurate & Precise
Computer Representation of
Numbers
 How do computers represent numbers?


Binary digits or bits or base 2
Groupings of bits into bytes and words
 How do we represent numbers?

Decimal system or base 10
 Need to understand how to convert between these number
systems
Base 10
1 2 4 0 5
5 x 100=
5
0 x 101=
00
4 x 102= 400
2 x 103= 2000
1 x 104= 10000
12405
Base 2
1 1 1 0 1
1 x 20=
1 = 1
0 x 21=
00 = 0
1 x 22= 100 = 4
1 x 23= 1000 = 8
1 x 24= 10000 = 16
11101
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