Question

The significant figures in \(500.5000\) are \(\ldots \ldots \ldots \ldots \ldots\) (a) 5 (b) 3 (c) 7 (d) 6

Short answer

The number of significant figures in \(500.5000\) is \(6\).

Step-by-step solution

Understand Significant Figures

Significant figures are simply non-zero digits or any trapped (sandwiched) zeros between nonzero digits in a number. Leading zeros (0's on the left side) are not considered significant, while trailing zeros (0's on the right side) after a decimal point are considered significant.

Identify Significant Figures in the Given Number

We have the number 500.5000. Let's identify the significant figures in this number: - Non-zero digits: 5 and 5 - Trapped zeros: None - Leading zeros: None - Trailing zeros after a decimal point: Four zeros (0000)

Count the Significant Figures

Now, let's count the significant figures in the number 500.5000: - Non-zero digits: 2 (5 and 5) - Trailing zeros after a decimal point: 4 (0000) Total significant figures: 2 + 4 = 6

Choose the Correct Answer

Based on our calculations, the number of significant figures in 500.5000 is 6. So the correct answer is: (d) 6

Key concepts

Understanding Non-Zero Digits

Non-zero digits are the backbone of any significant figure calculation. They are digits from 1 to 9 that appear in the number. For example, in the number 500.5000, the non-zero digits are the two fives present in the number: one before and one after the decimal point. These digits are always counted as significant because they contribute to the actual measured value of the number.

When we talk about non-zero digits, remember that:

• They are always considered significant.
• No matter where they appear in the number, whether before or after a decimal point.

Ensuring you count all non-zero digits is crucial in determining the total number of significant figures accurately.

Role of Trailing Zeros

Trailing zeros play a special role in the concept of significant figures, especially when they appear after a decimal point. In our example of 500.5000, the trailing zeros are the four zeros at the end, after the decimal point. These zeros are important because they show the precision of the measurement. When there are trailing zeros in a decimal number, they are considered significant.

Why are trailing zeros significant?

• They indicate the level of precision in the given measurement.
• They do not change the value of the number but provide information on accuracy.

In conclusion, all trailing zeros after a decimal point should be counted in significant figure calculations, as they enhance the clarity of how precise a given measurement is.

JEE Physics and Precision

JEE Physics often involves problems and calculations that require a precise understanding of significant figures. This is because physics calculations need accuracy to ensure results are reliable and meaningful. When handling numbers in JEE Physics, knowing how to apply significant figures can:

• Help you provide answers that reflect the true precision available in measurements.
• Ensure your calculations are consistent with the precision of the instruments used.

In JEE Physics, following these conventions allows students to communicate findings more effectively and ensures consistency when comparing results with theoretical predictions. Hence, getting comfortable with identifying significant figures, such as non-zero digits and trailing zeros, becomes an important skill in JEE Physics preparation.

Educational Problem Solving

Educational problem solving, especially in fields like physics, often demands more than just recalling formulas or definitions. It requires understanding concepts, like significant figures, and applying them correctly to various problems. By breaking down a problem into its core components, such as identifying non-zero digits and trailing zeros, students can:

• Improve their confidence in tackling numerical problems.


• Develop a deeper understanding that goes beyond rote memorization.

Approaching educational problem solving with a focus on principles, such as significant figures, equips students with the necessary tools to analyze, evaluate, and solve complex problems effectively. Ultimately, developing these problem-solving skills can lead to better academic performance and a more comprehensive grasp of the subject matter.