If (1 / 2.315) = 0.4319, find the value of (1 / 0.0002315).

Options

A. 4319
B. 2315
C. 431.9
D. 231.5

Answer

To solve the problem, we need to find the value of \( \frac{1}{0.0002315} \) given that \( \frac{1}{2.315} = 0.4319 \).

### Step-by-Step Solution:

1. **Understand the relationship between the numbers:**
We know that \( \frac{1}{2.315} = 0.4319 \). This means that \( 2.315 \) is the reciprocal of \( 0.4319 \).

2. **Convert \( 0.0002315 \) to a more manageable form:**
Notice that \( 0.0002315 \) can be expressed in terms of \( 2.315 \):
\[ 0.0002315 = \frac{2.315}{10000} \]
This is because moving the decimal point four places to the right gives us \( 2.315 \).

3. **Find the reciprocal of \( 0.0002315 \):**
To find \( \frac{1}{0.0002315} \), we can use the relation we established:
\[ \frac{1}{0.0002315} = \frac{1}{\frac{2.315}{10000}} = \frac{10000}{2.315} \]

4. **Use the known value of \( \frac{1}{2.315} \):**
Since we know \( \frac{1}{2.315} = 0.4319 \), we can substitute this into our equation:
\[ \frac{10000}{2.315} = 10000 \times \frac{1}{2.315} = 10000 \times 0.4319 \]

5. **Calculate the final value:**
Now we perform the multiplication:
\[ 10000 \times 0.4319 = 4319 \]

Thus, the value of \( \frac{1}{0.0002315} \) is **4319**.

### Final Answer:
\[ \frac{1}{0.0002315} = 4319 \]