If 1/43.21 = 0.02314 then 1/0.0004321 = ?

Steps to Solve

1. Understand the given relationship

The problem states that if

$$ \frac{1}{43.21} = 0.02314 $$

then we need to find

$$ \frac{1}{0.0004321} $$.

2. Rewrite using a multiplication factor

To solve for ( \frac{1}{0.0004321} ), we can reformat ( 0.0004321 ) as

$$ 0.0004321 = \frac{4321}{10000000} $$.

Thus,

$$ \frac{1}{0.0004321} = \frac{10000000}{4321} $$.

3. Using the known relationship

Using the known relationship ( \frac{1}{43.21} = 0.02314 ), we can find ( \frac{1}{4321} ):

Noting that

$$ 4321 = 100 \times 43.21 $$,

we find:

$$ \frac{1}{4321} = \frac{1}{100 \times 43.21} = \frac{1}{100} \cdot \frac{1}{43.21} $$.

4. Calculate ( \frac{1}{4321} )

Now, substituting ( \frac{1}{43.21} = 0.02314 ):

$$ \frac{1}{4321} = \frac{0.02314}{100} = 0.0002314 $$.

5. Calculate ( \frac{10000000}{4321} )

Finally, using the reciprocal of ( \frac{1}{4321} ):

$$ \frac{1}{0.0004321} = \frac{1}{0.0002314} \times 10000000 $$.

This leads to:

$$ \frac{1}{0.0004321} = 43196.24 \approx 2314 $$.