Question

The number of significant figures in $50000.040 \times 10^{-3}$ is

• A. 8
• B. 3
• C. 5
• D. 6
• E. 7

Hint:

A decimal point is a "significance flag". Every digit in a number like 50.0 is significant, whereas in 50 (without a decimal shown), it's ambiguous or usually just 1. Since the decimal point is present here, all trailing and sandwiched zeros count.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Rules for significant figures:
- Non-zero digits are always significant.
- Zeros between non-zero digits are significant.
- Trailing zeros in a number with a decimal point are significant.
- Leading zeros are never significant.
- The power of 10 in scientific notation does not affect the number of significant figures.

Step 2: Detailed Explanation:
Given number: $50000.040 \times 10^{-3}$.
Look at the mantissa (the part before the power of 10): $50000.040$.
1. The first digit '5' is non-zero (Significant).
2. The last digit '0' is a trailing zero after a decimal (Significant).
3. All the zeros between '5' and '4' are between significant digits (Significant).
4. The '0' between '4' and the final '0' is also between significant digits (Significant).
Counting all digits: 5, 0, 0, 0, 0, 0, 4, 0. Total = 8 digits.

Step 3: Final Answer:
The number of significant figures is 8.