Give that `3.718=(1)/(0.2689)`: then `(1)/(0.0003718)` is equal to

Options

A. 2689
B. `2.689`
C. 26890
D. `0.2689`

Answer

To solve the problem, we need to find the value of \(\frac{1}{0.0003718}\) given that \(3.718 = \frac{1}{0.2689}\).

### Step-by-Step Solution:

1. **Understanding the Given Equation**:
We start with the equation provided:
\[ 3.718 = \frac{1}{0.2689} \]
This implies that \(0.2689\) is the reciprocal of \(3.718\).

2. **Finding the Reciprocal**:
To find \(\frac{1}{0.0003718}\), we first need to understand the relationship between \(0.0003718\) and \(0.2689\). Notice that \(0.0003718\) can be expressed in terms of \(0.2689\).

3. **Shifting the Decimal**:
Since \(0.0003718\) has 4 decimal places, we can relate it to \(0.2689\) by multiplying \(0.2689\) by a factor of \(1000\) (to shift the decimal point to the right) and then dividing by \(1000\) to adjust for the decimal places:
\[ 0.0003718 = \frac{0.2689}{1000} \]

4. **Finding the Reciprocal**:
Now we can find the reciprocal of \(0.0003718\):
\[ \frac{1}{0.0003718} = \frac{1}{\frac{0.2689}{1000}} = \frac{1000}{0.2689} \]

5. **Calculating the Final Value**:
We already know from the given equation that:
\[ 3.718 = \frac{1}{0.2689} \]
Therefore:
\[ \frac{1000}{0.2689} = 1000 \times 3.718 \]
Now, we can calculate:
\[ 1000 \times 3.718 = 3718 \]

### Final Answer:
Thus, we find that:
\[ \frac{1}{0.0003718} = 3718 \]