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:
Significant figures are rules that determine which digits in a number carry actual meaning contributing to its measurement precision. We ignore exponential multipliers (like \(10^{-3}\)) when counting them.
Step 2: Key Formula or Approach:
Rule 1: All non-zero digits are significant.
Rule 2: Zeros between non-zero digits are significant.
Rule 3: In a number with a decimal point, trailing zeros are significant.
Step 3: Detailed Explanation:
The number given is \(50000.040 \times 10^{-3}\).
We only evaluate the coefficient part: \(50000.040\).
1) The digit '5' is a non-zero digit \(\rightarrow\) significant.
2) The digit '4' is a non-zero digit \(\rightarrow\) significant.
3) The four zeros between '5' and '4' are sandwiched between non-zero digits \(\rightarrow\) significant.
4) The final zero '0' comes after the decimal point and follows a non-zero digit, making it a trailing zero in a decimal number \(\rightarrow\) significant.
Counting them up: 5, 0, 0, 0, 0, 0, 4, 0. All 8 digits are significant.
Step 4: Final Answer:
There are 8 significant figures.