Solve the following with regard to the correct significant figures (i) `sqrt(4.8-2.35)` (ii) `2.35xx10^(3)-1.2xx10^(3)//2.0xx10^(2)`

Answer

To solve the given problems while considering significant figures, we will follow the rules for addition/subtraction and multiplication/division as outlined in the video transcript.

### Part (i): Solve `sqrt(4.8 - 2.35)`

1. **Perform the subtraction**:
\[ 4.8 - 2.35 = 2.45 \]

2. **Determine the significant figures**:
- The number 4.8 has 1 digit after the decimal.
- The number 2.35 has 2 digits after the decimal.
- According to the rule for subtraction, the result should have the least number of digits after the decimal, which is 1.

3. **Round the result to 1 decimal place**:
\[ 2.45 \approx 2.5 \]

4. **Take the square root**:
\[ \sqrt{2.5} \approx 1.5811 \]

5. **Round the square root result to 1 decimal place**:
\[ 1.5811 \approx 1.6 \]

**Final Answer for Part (i)**: 1.6

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### Part (ii): Solve `2.35 x 10^3 - 1.2 x 10^3 / 2.0 x 10^2`

1. **Perform the subtraction**:
\[ 2.35 \times 10^3 - 1.2 \times 10^3 = (2.35 - 1.2) \times 10^3 = 1.15 \times 10^3 \]

2. **Determine the significant figures**:
- The number 2.35 has 3 significant figures.
- The number 1.2 has 2 significant figures.
- According to the rule for subtraction, the result should have the least number of significant figures, which is 2.

3. **Round the result to 2 significant figures**:
\[ 1.15 \times 10^3 \approx 1.2 \times 10^3 \]

4. **Perform the division**:
\[ \frac{1.2 \times 10^3}{2.0 \times 10^2} = \frac{1.2}{2.0} \times 10^{3-2} = 0.6 \times 10^1 = 6.0 \]

5. **Determine the significant figures for the division**:
- The number 1.2 has 2 significant figures.
- The number 2.0 has 2 significant figures.
- According to the rule for multiplication/division, the result should have the least number of significant figures, which is 2.

6. **Final rounding**:
\[ 6.0 \text{ (already has 2 significant figures)} \]

**Final Answer for Part (ii)**: 6.0

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### Summary of Answers:
- Part (i): 1.6
- Part (ii): 6.0