`(24.23 xx 1.423 xx 34.21)/(521.3 xx 413.32 xx 2.53)` is same as

Options

A. `(2423 xx 1423 xx 3421)/(5213 xx 41332 xx253)`
B. `(242.3 xx 142.3 xx 3421)/(5213 xx 4133.2 xx2.53)`
C. `(2.423 xx14.23 xx342.1)/(521.3 xx 4133.2 xx 2.53)`
D. `(24.23 xx14.23 xx3.421)/(5.213 xx41332 xx0.253)`

Answer

To solve the expression \((24.23 \times 1.423 \times 34.21)/(521.3 \times 413.32 \times 2.53)\), we will convert the decimal numbers into fractions and simplify the expression step by step.

### Step 1: Convert decimals to fractions
We will convert each decimal number into a fraction.

- \(24.23 = \frac{2423}{100}\)
- \(1.423 = \frac{1423}{1000}\)
- \(34.21 = \frac{3421}{100}\)
- \(521.3 = \frac{5213}{10}\)
- \(413.32 = \frac{41332}{100}\)
- \(2.53 = \frac{253}{100}\)

### Step 2: Substitute the fractions into the expression
Now, we substitute these fractions into the original expression:

\[ \frac{\left(\frac{2423}{100} \times \frac{1423}{1000} \times \frac{3421}{100}\right)}{\left(\frac{5213}{10} \times \frac{41332}{100} \times \frac{253}{100}\right)} \]

### Step 3: Simplify the numerator and denominator
**Numerator:**
\[ \frac{2423 \times 1423 \times 3421}{100 \times 1000 \times 100} = \frac{2423 \times 1423 \times 3421}{10^6} \]

**Denominator:**
\[ \frac{5213 \times 41332 \times 253}{10 \times 100 \times 100} = \frac{5213 \times 41332 \times 253}{10^4} \]

### Step 4: Combine the fractions
Now, we can combine the fractions:

\[ \frac{2423 \times 1423 \times 3421}{10^6} \div \frac{5213 \times 41332 \times 253}{10^4} = \frac{2423 \times 1423 \times 3421}{5213 \times 41332 \times 253} \times \frac{10^4}{10^6} \]

This simplifies to:

\[ \frac{2423 \times 1423 \times 3421}{5213 \times 41332 \times 253} \times \frac{1}{10^2} = \frac{2423 \times 1423 \times 3421}{5213 \times 41332 \times 253} \times \frac{1}{100} \]

### Step 5: Final expression
Thus, the final expression can be written as:

\[ \frac{2423 \times 1423 \times 3421}{5213 \times 41332 \times 253} \times \frac{1}{100} \]

### Conclusion
The expression \((24.23 \times 1.423 \times 34.21)/(521.3 \times 413.32 \times 2.53)\) is equivalent to:

\[ \frac{2423 \times 1423 \times 3421}{5213 \times 41332 \times 253} \times \frac{1}{100} \]