State the number of significant figures in the following measurements :
(i) `0.009 m^(2) " " (ii) 5.049 N m^(-2) " " (iii) 0.1890 g cm^(-3) " " (iv) 1.90 xx 10^(11) kg " " (v) 0.020800 m " " (vi) 5.308 J `

Answer

To determine the number of significant figures in each measurement, we follow specific rules regarding significant figures. Here’s the step-by-step solution for each measurement:

### Step-by-Step Solution:

1. **Measurement: 0.009 m²**
- The leading zeros (0.00) are not significant.
- The significant figure is only the '9'.
- **Significant Figures: 1**

2. **Measurement: 5.049 N m⁻²**
- All non-zero digits are significant.
- The digits '5', '0', '4', and '9' are all significant.
- **Significant Figures: 4**

3. **Measurement: 0.1890 g cm⁻³**
- The leading zero (0.) is not significant.
- The digits '1', '8', '9', and the trailing zero (0) after the decimal point are significant.
- **Significant Figures: 4**

4. **Measurement: 1.90 x 10⁻¹¹ kg**
- The power of ten does not affect the count of significant figures.
- The digits '1', '9', and '0' are all significant.
- **Significant Figures: 3**

5. **Measurement: 0.020800 m**
- The leading zeros (0.0) are not significant.
- The digits '2', '0', '8', and the two trailing zeros (00) after the decimal point are significant.
- **Significant Figures: 5**

6. **Measurement: 5.308 J**
- All digits are non-zero and thus significant.
- The digits '5', '3', '0', and '8' are all significant.
- **Significant Figures: 4**

### Summary of Significant Figures:
- (i) 0.009 m²: **1**
- (ii) 5.049 N m⁻²: **4**
- (iii) 0.1890 g cm⁻³: **4**
- (iv) 1.90 x 10⁻¹¹ kg: **3**
- (v) 0.020800 m: **5**
- (vi) 5.308 J: **4**