Find the value of`(547527)/(82),`if `(547.527)/(0.0082)= x.`

Options

A. 10 x
B. 100 x
C. `(x)/(100)`
D. `(x)/(10)`

Answer

To solve the problem, we need to find the value of \( \frac{547527}{82} \) given that \( \frac{547.527}{0.0082} = x \).

### Step-by-Step Solution:

1. **Understanding the relationship between the two fractions**:
We start with the equation:
\[ \frac{547.527}{0.0082} = x \]
We can manipulate this equation to express \( x \) in terms of \( \frac{547527}{82} \).

2. **Convert the decimal to a whole number**:
Notice that \( 547.527 \) can be expressed as \( \frac{547527}{1000} \) and \( 0.0082 \) can be expressed as \( \frac{82}{10000} \). Thus, we can rewrite the fraction:
\[ \frac{547.527}{0.0082} = \frac{\frac{547527}{1000}}{\frac{82}{10000}} = \frac{547527 \times 10000}{82 \times 1000} \]

3. **Simplifying the expression**:
This simplifies to:
\[ \frac{547527 \times 10}{82} \]
Therefore, we have:
\[ x = \frac{5475270}{82} \]

4. **Finding \( \frac{547527}{82} \)**:
From the above equation, we can express \( \frac{547527}{82} \) as follows:
\[ \frac{547527}{82} = \frac{x}{10} \]

5. **Calculating the final value**:
Since we need to find \( \frac{547527}{82} \), we can now calculate it using the value of \( x \):
\[ \frac{547527}{82} = \frac{547.527}{0.0082} \div 10 \]

6. **Final Calculation**:
To find the numerical value of \( x \):
\[ x = \frac{547.527}{0.0082} = 66750 \]
Therefore:
\[ \frac{547527}{82} = \frac{66750}{10} = 6675 \]

### Final Answer:
The value of \( \frac{547527}{82} \) is \( 6675 \).