Error Discussion: Types, Causes, and Solutions

"Understand different types of errors in programming, computation, and data processing. This guide explores common errors, their causes, debugging techniques, and best practices for error handling to ensure efficient and reliable systems."

1. Error Discussion

2. Error Error in solving an engineering or science problem can arise due to several factors. First, the error may be in the modelling technique. A mathematical model may be based on using assumptions that are not acceptable. Second, errors may arise from mistakes in programs themselves or in the measurement of physical quantities.

3. Errors Absolute error 01 Relative error 02 Percentage error 03 Round off error 04 Truncation error. 05

4. Absolute Error: E A = | X-x | Here, X = exact value x = approximate value Absolute error is defined as the difference between the actual value and the measured value of a quantity. The importance of absolute error depends on the quantity that we are measuring. If the quantity is large such as road distance, a small error in centimetres is negligible. While measuring the length of a machine part an error in centimetre is considerable. Though the errors in both cases are in centimetres, the error in the second case is more important.

5. Relative Error:   The ratio of absolute error of the measurement and the actual value is called relative error. By calculating the relative error, we can have an idea of how good the measurement is compared to the actual size. From the relative error, we can determine the magnitude of absolute error. If the actual value is not available, the relative error can be calculated in terms of the measured value of the quantity. The relative error is dimensionless and it has no unit.

6. Percentage Error: E p = 100E R Percent errors indicate how big our errors are when we measure something in an analysis process. Smaller percent errors indicate that we are close to the accepted or original value. For example, a 1% error indicates that we got very close to the accepted value, while 48% means that we were quite a long way off from the true value. Measurement errors are often unavoidable due to certain reasons like hands can shake, material can be imprecise, or our instruments just might not have the capability to estimate exactly.  Percent error formula  will let us know how seriously these inevitable errors influenced our results.

7. Round off Error Rounding error is the difference between a rounded-off numerical value and the actual value. A rounded quantity is represented by a numeral with a fixed number of allowed digits, with the last digit set to the value that produces the smallest difference between the rounded quantity and the actual quantity.

8.   Truncation Error:

9. Significant Digits: Significant figures (also known as the significant digits, precision or resolution) of a number in positional notation are digits in the number that are reliable and absolutely necessary to indicate the quantity of something. Rule 1: Every non-zero digit is significant 456 has 3 significant digits Rule 2: Zeros between non-zero digits are always significant 5,609 has 4 significant digits. Rule 3: Zeros before non-zero digits are never significant 0.067 has 2 significant digits Rule 4: Zeros behind non-zero digits are sometimes significant 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0.

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