If `(1)/(43.21)=0.02314` then `(1)/(0.0004321)=?`

Options

A. 23.14
B. 2314
C. 0.0002314
D. 231.4

Answer

To solve the problem, we need to find the value of \( \frac{1}{0.0004321} \) using the information given that \( \frac{1}{43.21} = 0.02314 \).

### Step 1: Understand the relationship between the two fractions

We know that \( 0.0004321 \) can be expressed in terms of \( 43.21 \). Specifically, we can rewrite \( 0.0004321 \) as:

\[ 0.0004321 = \frac{4321}{10000000} \]

### Step 2: Find the reciprocal of \( 0.0004321 \)

To find \( \frac{1}{0.0004321} \), we can use the reciprocal of the fraction we just formed:

\[ \frac{1}{0.0004321} = \frac{10000000}{4321} \]

### Step 3: Relate \( \frac{10000000}{4321} \) to \( \frac{1}{43.21} \)

Since we know \( \frac{1}{43.21} = 0.02314 \), we can express \( 4321 \) in terms of \( 43.21 \):

\[ 4321 = 43.21 \times 100 \]

Thus, we can rewrite \( \frac{10000000}{4321} \):

\[ \frac{10000000}{4321} = \frac{10000000}{43.21 \times 100} = \frac{100000}{43.21} \]

### Step 4: Calculate \( \frac{100000}{43.21} \)

Now, we can calculate \( \frac{100000}{43.21} \) using the value of \( \frac{1}{43.21} \):

\[ \frac{100000}{43.21} = 100000 \times \frac{1}{43.21} = 100000 \times 0.02314 \]

### Step 5: Perform the multiplication

Now we perform the multiplication:

\[ 100000 \times 0.02314 = 2314 \]

### Final Answer

Thus, the value of \( \frac{1}{0.0004321} \) is:

\[ \frac{1}{0.0004321} = 2314 \]