When uising a number in a calculation ther must be assurance that can be used with confidence.The Concept of Significant figures has two important implications in the study of numerical methods.
- The Numerical Methods obtain approximate results. Therefore criterion should be developed to specify how accurate are the results obtained.
- Although some numbers represent specific number can be expressed exactly.
The significant figures of a number are those that can be used with confidence. They correspond to the numbers of certain digits plus one estimated digit.
Example
pi= 3,14159265358979......
Because the computer retains only a finite numbers of signicant figures, such number can ever be represent exactly. The omission of the remaining figures is called round-off error.
Accuracy and Precision ( Watch Video)
The error in calculations and measures can be characterized with regard to their accuracy and precision. Accuracy refers to how closely a computed or measured value agrees with the tre value. Precision refers to how closely individual computed or measured values agree with each other.
Inaccuracy is defined as systematic deviation from the truth. The Imprecision refers to the dispersion.
Error Definitions and The Taylor Series ( Document ) ( Excel )
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