Numerical approximation

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2. 3. 4. 5. 1 6. 2 7. 1 All nonzero digits are significant: 1,284 g Has 4 significant figures 1,2 g Has 2 significant figures With zeroes, the situation is particularly: 2 Zeroes placed before other digits are not significant. 0.046 Has two significant digits. 8. 4009kgHas four significant digits. 3 Zeroes placed between other digits are always significant. 4 Zeroes placed after other digits but behind a decimal point are significant.7,90 Has three significant digits. 9. 8.200 x10 3 4 S.F 8.20 x10 3 3 S.F 8.2 x 1 0 3 2 S.F 5 Zeroes at the end of a number are significant only if they are behind a decimal point. Otherwise, it is impossible to tell if they are significant. For example, in the number 8200, it is not clear if the zeroes are significant or not. The number of significant digits in 8200 is at least two, but could be three or four. To avoid uncertainty, use scientific notation to place significant zeroes behind a decimal point: 10. In math operations, the significant numberits in answer should equal to the least number of significant digits in any one of the numbers being multiplied, divided etc. ( 3 S.F) (2 S.F) (4 S.F) (2 S.F) 11. 1 If the digit removed is greater than 5, the previous digit increases by one. E.g:8.236-> 8.24 2 If the digit removed is less than 5, the previous digit is not modified.E.g:8.231-> 8.23 3 If the digit removed is 5 followed by a different number than 0, the previous digit increases by one. E.g:8.2353->8.24 4 If the digit removed is 5 followed by 0 looks to the next that follows, if it is odd increase or if its pair remains unchanged. E.g: (1)8.23503->8.24 (2)8.23502->8.23 12. 13. ACCURACY refers to how close is measured or calculated value to the true value. PRECISION refers to how close is an measured or calculated individual valuewith respect to the others. THE INACCURACY OR BIAS is defined as a systematic departure from the truth. THE VAGUENESS OR UNCERTAINTY , refers to the magnitude of the spread of values. d b c a 14. The numerical methods should be sufficiently accurate or no bias to satisfy the requirements of a particular engineering problem . 15. 16. For the types of errors, the relationship between the exact or true result and the approximate is given by: True value = Approximation + error 17.

          • Relative Error
  • It is the quotient (division) between the absolute error and the true value.If you multiply by 100 to obtain the true percentage relative error.
  • True or Absolute Error
  • It isequal to the difference between the true value and approximate value

or 18. 19. 20. Aproximacin de la funcin exponencial Fuente: 21. 22. 23. With the Taylor series we can estimate the truncation errors 24.