Significant Figures

To solve this problem, we need to match numbers from List - I with their corresponding significant figures from List - II. Here's how we can determine the number of significant figures for each number:

1. Number 1001:
   • This number does not contain any leading or trailing zeros that are not significant. It has four non-zero digits.
   • Therefore, it has significant figures.
2. Number 010.1:
   • The leading zero before 10.1 is not significant. The digits '10.1' are significant.
   • Hence, it has significant figures.
3. Number 100.100:
   • This number has trailing zeros after the decimal point, making them significant. All digits are significant.
   • Thus, it has significant figures.
4. Number 0.0010010:
   • The leading zeros (0.00) are not significant, but zeros at the end of the decimal places with non-zero digits are significant.
   • Therefore, it has significant figures.

Based on our analysis, the correct matching is:

1. (A) 1001 - (II) 4 significant figures.
2. (B) 010.1 - (I) 3 significant figures.
3. (C) 100.100 - (IV) 6 significant figures.
4. (D) 0.0010010 - (III) 5 significant figures.

The correct option is: (A)-(II), (B)-(I), (C)-(IV), (D)-(III).

Sum of the numbers, considering the correct significant figures:

The arithmetic mean is:

The result is rounded to the correct significant figure.

To solve the problem, we need to evaluate the expression and determine the correct number of significant figures in the result. The given expression is:

To determine the final number of significant figures, follow these steps:

1. Identify the number of significant figures in each term:
   • has 3 significant figures.
   • has 4 significant figures.
   • has 3 significant figures.
2. Multiply by . The product will have the smallest number of significant figures present in the multiplied numbers, which is 3.
   • Calculation: (but retain 3 significant figures only).
   • Rounded to 3 significant figures: .
3. Divide the result by :
   • Calculation:
   • Since the division involves 3 significant figures from both the numerator and the denominator, we round the result to 3 significant figures.
4. Round to 3 significant figures: .

Therefore, the value of should be reported as:

• .

This solution uses correct significant figure rules and arithmetic to arrive at the answer , matching the given correct option.