Question

If the length of a rod is measured as 830600 mm, then the number of significant figures in the measurement is

• A. 5
• B. 3
• C. 6
• D. 4

Hint:

To avoid ambiguity with trailing zeros, it's best to express the number in scientific notation. In this case, \(8.306 \times 10^5\) mm clearly shows 4 significant figures. If it were written as \(8.30600 \times 10^5\) mm, it would have 6 significant figures.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Significant figures are the digits in a number that are reliable and necessary to indicate the quantity of something. They include all certain digits plus one uncertain digit.
Step 2: Key Rules for Significant Figures:
1. All non-zero digits are significant.
2. Zeros between two non-zero digits are significant.
3. Leading zeros (zeros before non-zero numbers) are not significant.
4. Trailing zeros (zeros at the end of the number) are significant only if the number contains a decimal point.
Step 3: Detailed Explanation:
Let's apply these rules to the number 830600 mm.
- The digits 8, 3, and 6 are non-zero, so they are significant. (3 significant figures so far).
- The zero between 3 and 6 is a captive zero (Rule 2), so it is also significant. (4 significant figures so far: 8, 3, 0, 6).
- The last two zeros (the '00' at the end) are trailing zeros. Since the number 830600 does not have a decimal point, these trailing zeros are not considered significant (Rule 4). They are simply placeholders to indicate the magnitude of the number.
Thus, the significant digits are 8, 3, 0, and 6.
Step 4: Final Answer:
The total count of significant figures in the measurement 830600 mm is 4. Therefore, option (D) is the correct answer.