Understanding Significant Figures in Scientific Calculations: A Deep Dive
The concept of significant figures is crucial in scientific calculations, providing a standardized method to determine the precision and accuracy of numerical values. This article aims to clarify the reasoning behind the number of significant figures in the expression 50000.020 × 10-3, as declared by the National Testing Agency (NTA) for JEE Mains 2021.
Significance of Each Digit
Let's start by breaking down the number 50000.020. In determining the number of significant figures, we follow these rules:
Non-zero digits are always significant. Zeros between non-zero digits are significant. Zeros at the end of a number and to the right of the decimal point are significant. Zeros at the end of a number without a decimal point are not significant unless specified otherwise.Therefore, in the number 50000.020:
The digits 5, 0, 0, 0, 0, and 2 are significant. The trailing zeros after the decimal point (0.020) are also significant because they come after a non-zero digit.Following these rules, we can conclude that the number 50000.020 has a total of 8 significant figures.
Scientific Notation and Significant Figures
The expression 50000.020 × 10-3 is in scientific notation. Scientific notation helps express very large or very small numbers in a more manageable form. However, the rules for significant figures in scientific notation don't change. The number 50000.020 × 10-3 is equivalent to 50.00002, and the significant figures remain the same as in 50000.020.
Therefore, the number 50000.020 × 10-3 still has 8 significant figures.
The Discrepancy with JEE Mains 2021 NTA Answer
Given that the analysis above shows 8 significant figures, the answer provided by JEE Mains 2021 NTA as 7 significant figures appears to be incorrect. This discrepancy raises important questions about the accuracy and consistency of the evaluation process.
Based on the rules of significant figures, you may consider challenging the answer. A clear and well-supported explanation that 50000.020 has 8 significant figures can strengthen your argument.
The expression 50000.020 × 10-3 can be simplified to 50.00002. Here, 5000002 would have 7 significant figures, but since we have a trailing zero after the decimal point, it adds one more significant figure, making it 8.
Significance of Sign Figures in Practical Applications
Understanding and correctly applying the concept of significant figures is essential in scientific and engineering contexts. It ensures that results are reported with appropriate precision, reflecting the true accuracy of the measurements and calculations.
Here are a few practical examples where significant figures play a crucial role:
Physics Experiments: In experiments, the number of significant figures determines the reliability of the results and helps avoid misinterpretation. Chemistry: In chemical calculations, significant figures help in determining the accuracy of the final answer. Engineering: In design and analysis, the precision of significant figures is critical for material strength calculations and safety considerations.To ensure accurate reporting and avoid confusion, it is crucial to follow the rules of significant figures consistently.
Conclusion: The number of significant figures in 50000.020 × 10-3 is 8. If JEE Mains 2021 NTA marked the answer as 7, it might be necessary to challenge this decision with a clear explanation of the significant figures rules.