12 Questions
What is the result of rounding off 865250 to 4 significant figures?
865200
What is the primary objective of numerical methods in solving problems?
To provide an approximate solution
What type of error occurs when a number is approximated by a smaller number of digits?
Truncation error
What is the result of rounding off 7.893 to 3 significant figures?
7.9
Why are numerical methods used in solving problems?
Because analytical methods are not feasible
What is the result of rounding off 0.000029673 to 4 significant figures?
3.0E-5
What is the purpose of rounding off numbers in numerical methods?
To obtain an approximate value with a specified number of significant figures.
How do analytical methods differ from numerical methods in solving problems?
Analytical methods provide exact solutions, whereas numerical methods provide approximate solutions.
What is the distinction between inherent error and truncation error in numerical methods?
Inherent error is the error in the original data, while truncation error is the error introduced by rounding off numbers.
When might numerical methods be more suitable than analytical methods in solving problems?
When the problem is too complicated or the exact solution is difficult to obtain.
Why are numerical methods necessary in solving problems that involve tabulated data?
Because the data may not be exact, and numerical methods can provide an approximate solution.
What is the significance of the number of significant figures in numerical methods?
It determines the accuracy of the approximate solution obtained.
Explore the practical limitations of numerical methods in engineering and science, including rounding off errors and significant figures. Learn how to properly round off numbers and manage errors in calculations.
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