Show with regards to significant figure
(i) 908 + 2.76
(ii) 999-989
(iii) `4.0 xx 10^(4) - 2.5 xx 10^(2)`
(iv) `4.0 xx 10^(4) - 2.5 xx 10^(5)`
(v) `6.75 xx 10^(3) + 4.52 xx 10^(2)`
(vi) 625 + 125

Answer

To solve the given problems regarding significant figures, we will follow the rules of significant figures during addition and subtraction. The key points to remember are:

1. In addition and subtraction, the result should be reported to the least number of decimal places of any number in the operation.
2. In multiplication and division, the result should have the same number of significant figures as the number with the least significant figures.

Now, let's solve each part step by step:

### (i) 908 + 2.76
1. **Perform the addition**:
\[ 908 + 2.76 = 910.76 \]
2. **Determine significant figures**:
- 908 has 3 significant figures (the last digit is not a decimal).
- 2.76 has 3 significant figures (it has two decimal places).
3. **Round the result**:
- The answer should be rounded to the least number of decimal places, which is 0 (from 908).
- Thus, 910.76 rounds to 911.

**Final Answer**: 911

### (ii) 999 - 989
1. **Perform the subtraction**:
\[ 999 - 989 = 10 \]
2. **Determine significant figures**:
- Both 999 and 989 have 3 significant figures.
3. **Round the result**:
- The answer is 10, which has 2 significant figures. However, since both original numbers had 3 significant figures, we should express it as 10.0 to maintain 3 significant figures.

**Final Answer**: 10.0

### (iii) \(4.0 \times 10^{4} - 2.5 \times 10^{2}\)
1. **Rewrite the second term**:
\[ 2.5 \times 10^{2} = 0.025 \times 10^{4} \]
2. **Perform the subtraction**:
\[ 4.0 \times 10^{4} - 0.025 \times 10^{4} = 3.975 \times 10^{4} \]
3. **Determine significant figures**:
- 4.0 has 2 significant figures.
- 0.025 has 2 significant figures.
4. **Round the result**:
- The answer should be rounded to 2 significant figures: 3.975 rounds to 4.0.

**Final Answer**: \(4.0 \times 10^{4}\)

### (iv) \(4.0 \times 10^{4} - 2.5 \times 10^{5}\)
1. **Rewrite the first term**:
\[ 4.0 \times 10^{4} = 0.40 \times 10^{5} \]
2. **Perform the subtraction**:
\[ 0.40 \times 10^{5} - 2.5 \times 10^{5} = -2.10 \times 10^{5} \]
3. **Determine significant figures**:
- Both terms have 2 significant figures.
4. **Round the result**:
- The answer rounds to -2.1 (neglecting the zero).

**Final Answer**: \(-2.1 \times 10^{5}\)

### (v) \(6.75 \times 10^{3} + 4.52 \times 10^{2}\)
1. **Rewrite the second term**:
\[ 4.52 \times 10^{2} = 0.452 \times 10^{3} \]
2. **Perform the addition**:
\[ 6.75 \times 10^{3} + 0.452 \times 10^{3} = 7.202 \times 10^{3} \]
3. **Determine significant figures**:
- 6.75 has 3 significant figures.
- 0.452 has 3 significant figures.
4. **Round the result**:
- The answer should be rounded to 3 significant figures: 7.202 rounds to 7.20.

**Final Answer**: \(7.20 \times 10^{3}\)

### (vi) 625 + 125
1. **Perform the addition**:
\[ 625 + 125 = 750 \]
2. **Determine significant figures**:
- Both 625 and 125 have 3 significant figures.
3. **Final answer**:
- Since both numbers have the same significant figures, the answer remains as is.

**Final Answer**: 750

### Summary of Final Answers:
1. 911
2. 10.0
3. \(4.0 \times 10^{4}\)
4. \(-2.1 \times 10^{5}\)
5. \(7.20 \times 10^{3}\)
6. 750