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Numerical Methods in Engineering and Science

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Numerical Methods in Engineering and Science

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Questions and Answers

What is the result of rounding off 865250 to 4 significant figures?

865300
865200 (correct)
865000
865250

What is the primary objective of numerical methods in solving problems?

To eliminate the error
To find the exact solution
To simplify the problem
To provide an approximate solution (correct)

What type of error occurs when a number is approximated by a smaller number of digits?

Truncation error (correct)
Inherent error
Approximation error
Rounding off error

What is the result of rounding off 7.893 to 3 significant figures?

7.9 (C) Signup and view all the answers

Why are numerical methods used in solving problems?

Because analytical methods are not feasible (B) Signup and view all the answers

What is the result of rounding off 0.000029673 to 4 significant figures?

3.0E-5 (A), 3.0E-5 (B), 3.0E-5 (D) Signup and view all the answers

What is the purpose of rounding off numbers in numerical methods?

To obtain an approximate value with a specified number of significant figures. Signup and view all the answers

How do analytical methods differ from numerical methods in solving problems?

Analytical methods provide exact solutions, whereas numerical methods provide approximate solutions. Signup and view all the answers

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. Signup and view all the answers

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. Signup and view all the answers

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. Signup and view all the answers

What is the significance of the number of significant figures in numerical methods?

It determines the accuracy of the approximate solution obtained. Signup and view all the answers