How many significant figures are there in each of the following numbers?
`(i)6.200" "(ii)0.052" "(iii)7.5xx10^(4)" "(iv) 0.00050" "(v) 67.32-6.3" "(vi) 4.2+7.589`
`(vii)(5.56)^(2)(8.24)//(3.6)" "(viii)18.567//(8.1xx2)`

Explanation

To determine the number of significant figures in each of the given numbers, we will analyze each number based on the rules of significant figures. Here’s the step-by-step solution:

### Solution:

**(i) 6.200**
- The digits are 6, 2, 0, 0.
- All non-zero digits are significant.
- Zeros between significant digits and trailing zeros in a decimal number are also significant.
- **Total significant figures = 4.**

**(ii) 0.052**
- The digits are 5, 2.
- Leading zeros (0.0) are not significant.
- **Total significant figures = 2.**

**(iii) 7.5 x 10^4**
- The digits are 7 and 5.
- In scientific notation, only the digits in the coefficient (7.5) are counted.
- **Total significant figures = 2.**

**(iv) 0.00050**
- The digits are 5, 0.
- Leading zeros are not significant, but the trailing zero after 5 is significant.
- **Total significant figures = 2.**

**(v) 67.32 - 6.3**
- The result of the subtraction is 61.02.
- When performing subtraction, the result should be rounded to the least number of decimal places in the original numbers.
- 67.32 has 2 decimal places, and 6.3 has 1 decimal place.
- Thus, the result should be rounded to 1 decimal place: 61.0.
- **Total significant figures = 3.**

**(vi) 4.2 + 7.589**
- The result of the addition is 11.829.
- The number 4.2 has 1 decimal place, while 7.589 has 3 decimal places.
- Thus, the result should be rounded to 1 decimal place: 11.8.
- **Total significant figures = 3.**

**(vii) (5.56)^2 * (8.24) / (3.6)**
- The significant figures are:
- 5.56 has 3 significant figures.
- 8.24 has 3 significant figures.
- 3.6 has 2 significant figures.
- The result will have the same number of significant figures as the measurement with the least significant figures, which is 3.6.
- **Total significant figures = 2.**

**(viii) 18.567 / (8.1 x 2)**
- The significant figures are:
- 18.567 has 5 significant figures.
- 8.1 has 2 significant figures.
- The result will have the same number of significant figures as the measurement with the least significant figures, which is 8.1.
- **Total significant figures = 2.**

### Summary of Significant Figures:
1. 6.200 → 4 significant figures
2. 0.052 → 2 significant figures
3. 7.5 x 10^4 → 2 significant figures
4. 0.00050 → 2 significant figures
5. 67.32 - 6.3 → 3 significant figures
6. 4.2 + 7.589 → 3 significant figures
7. (5.56)^2 * (8.24) / (3.6) → 2 significant figures
8. 18.567 / (8.1 x 2) → 2 significant figures