State the number of significant figures in each of the following:
(i) 136.7 m (ii) 105.67 kg
(iii) `3.4 xx 10^(6)s` (iv) 0.0078 km
(v) `0.00650 xx 10^(6) m`

Answer

To determine the number of significant figures in each of the given measurements, we will follow the rules of significant figures:

1. **All non-zero digits are significant.**
2. **Any zeros between significant digits are significant.**
3. **Leading zeros (zeros before the first non-zero digit) are not significant.**
4. **Trailing zeros in a decimal number are significant.**
5. **In scientific notation, all digits in the coefficient are significant.**

Now, let's analyze each measurement step by step:

### (i) 136.7 m
- **Step 1:** Identify the digits: 1, 3, 6, and 7.
- **Step 2:** Count the significant figures: All four digits are non-zero.
- **Conclusion:** The number of significant figures is **4**.

### (ii) 105.67 kg
- **Step 1:** Identify the digits: 1, 0, 5, 6, and 7.
- **Step 2:** Count the significant figures: The zero is between 1 and 5, so it is significant, along with the other non-zero digits.
- **Conclusion:** The number of significant figures is **5**.

### (iii) 3.4 × 10^6 s
- **Step 1:** Identify the digits in the coefficient: 3 and 4.
- **Step 2:** Count the significant figures: Both digits are non-zero.
- **Conclusion:** The number of significant figures is **2**.

### (iv) 0.0078 km
- **Step 1:** Identify the digits: 7 and 8.
- **Step 2:** Count the significant figures: The leading zeros (0.00) are not significant.
- **Conclusion:** The number of significant figures is **2**.

### (v) 0.00650 × 10^6 m
- **Step 1:** Rewrite in standard form: 6.50 × 10^3 m.
- **Step 2:** Identify the digits in the coefficient: 6, 5, and the trailing zero.
- **Step 3:** Count the significant figures: All digits in the coefficient are significant.
- **Conclusion:** The number of significant figures is **3**.

### Summary of Significant Figures:
1. 136.7 m → **4 significant figures**
2. 105.67 kg → **5 significant figures**
3. 3.4 × 10^6 s → **2 significant figures**
4. 0.0078 km → **2 significant figures**
5. 0.00650 × 10^6 m → **3 significant figures**

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