An analytical balance has uncertainity in measurement equal to `pm1` mg. Then the result in terms of persentage would be if the weight of a compound is 10 g

Options

A. `10pm0.1%`
B. `10pm0.01%`
C. `10pm1%`
D. `10pm0.001%`

Answer

To solve the problem, we need to determine the percentage uncertainty in the measurement of the weight of a compound using the given data.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Weight of the compound (W) = 10 g
- Uncertainty in measurement (ΔW) = ±1 mg

2. **Convert Uncertainty from Milligrams to Grams**:
- Since 1 mg = 0.001 g, we convert the uncertainty:
\[ \Delta W = 1 \text{ mg} = 1 \times 10^{-3} \text{ g} = 0.001 \text{ g} \]

3. **Express the Measurement with Uncertainty**:
- The weight of the compound can be expressed as:
\[ W = 10 \text{ g} \pm 0.001 \text{ g} \]

4. **Calculate the Percentage Uncertainty**:
- The percentage uncertainty is calculated using the formula:
\[ \text{Percentage Uncertainty} = \left(\frac{\Delta W}{W}\right) \times 100 \]
- Substitute the values:
\[ \text{Percentage Uncertainty} = \left(\frac{0.001 \text{ g}}{10 \text{ g}}\right) \times 100 \]

5. **Perform the Calculation**:
- Calculate the fraction:
\[ \frac{0.001}{10} = 0.0001 \]
- Now multiply by 100 to get the percentage:
\[ 0.0001 \times 100 = 0.01\% \]

6. **Final Result**:
- The percentage uncertainty in the measurement of the weight of the compound is:
\[ \text{Percentage Uncertainty} = 0.01\% \]

### Summary:
The result in terms of percentage uncertainty for the weight of the compound (10 g) with an uncertainty of ±1 mg is **0.01%**.

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