If `(1)/((3.197))=0.3127` find the value of `(1)/((0.0003197))`

Options

A. 3127
B. 3197
C. `312.7`
D. `0.3127`

Answer

To solve the problem of finding the value of \( \frac{1}{0.0003197} \) given that \( \frac{1}{3.197} = 0.3127 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**: We know that \( \frac{1}{3.197} = 0.3127 \).

2. **Manipulate the Denominator**: We want to find \( \frac{1}{0.0003197} \). To relate this to the known value, we can manipulate \( 0.0003197 \) to express it in terms of \( 3.197 \).

3. **Convert \( 0.0003197 \)**: We can multiply and divide \( 0.0003197 \) by \( 10,000 \) to shift the decimal point:
\[ 0.0003197 \times 10,000 = 3.197 \]
Thus, we have:
\[ 0.0003197 = \frac{3.197}{10,000} \]

4. **Substituting Back**: Now we can rewrite \( \frac{1}{0.0003197} \) using the expression we found:
\[ \frac{1}{0.0003197} = \frac{1}{\frac{3.197}{10,000}} = \frac{10,000}{3.197} \]

5. **Using the Known Value**: Now we can substitute the known value \( \frac{1}{3.197} = 0.3127 \):
\[ \frac{10,000}{3.197} = 10,000 \times \frac{1}{3.197} = 10,000 \times 0.3127 \]

6. **Calculate the Final Value**: Now we multiply:
\[ 10,000 \times 0.3127 = 3127 \]

### Conclusion:
Thus, the value of \( \frac{1}{0.0003197} \) is \( 3127 \).