Choose the correct alternative (s) from the following .

Options

A. The number of significant figures in 0.080 is 2.
B. The number of significant figure is `3.04 xx 10^(23)` is 25
C. The number of significant figures in 0.01020 is 4.
D. The number of significant figures in `4.06 xx 10 ^(-4)` is 3.

Answer

To solve the question regarding significant figures, we will analyze each option based on the rules of significant figures. Here’s a step-by-step breakdown:

### Step 1: Understand the Rules of Significant Figures
1. **Zeros between non-zero digits are significant.**
2. **Leading zeros to the left of the first non-zero digit are not significant.**
3. **Trailing zeros that are to the right of a decimal point in a number are significant.**

### Step 2: Analyze Each Option

#### Option A: 0.080
- The number is 0.080.
- According to the rules:
- The leading zeros (0 before 8) are not significant.
- The trailing zero (0 after 8) is significant.
- Significant figures: 2 (the digits 8 and the trailing 0).
- **Conclusion**: This option is **correct**.

#### Option B: 3.04 x 10^23
- The number is 3.04.
- According to the rules:
- The zero between 3 and 4 is significant.
- Significant figures: 3 (the digits 3, 0, and 4).
- **Conclusion**: This option states there are 2 significant figures, which is **incorrect**.

#### Option C: 0.01020
- The number is 0.01020.
- According to the rules:
- The leading zeros (0s before 1) are not significant.
- The trailing zeros (0 after 2) are significant.
- Significant figures: 4 (the digits 1, 2, and the trailing 0).
- **Conclusion**: This option is **correct**.

#### Option D: 4.06 x 10^-4
- The number is 4.06.
- When written in decimal form, it is 0.000406.
- According to the rules:
- The leading zeros (0s before 4) are not significant.
- The zero between 4 and 6 is significant.
- Significant figures: 3 (the digits 4, 0, and 6).
- **Conclusion**: This option is **correct**.

### Final Conclusion
- The correct alternatives are:
- **Option A**: Correct (2 significant figures)
- **Option C**: Correct (4 significant figures)
- **Option D**: Correct (3 significant figures)
- **Option B**: Incorrect (3 significant figures)

### Summary of Answers:
- Correct options: A, C, D
- Incorrect option: B