The fractional equivalent of 57.12% (approx.) is

Options

A. `(359)/(625)`
B. `(357)/(625)`
C. `(347)/(625)`
D. `(349)/(625)`

Answer

To find the fractional equivalent of 57.12%, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Percentage to a Fraction**:
- The percentage 57.12% can be written as a fraction by placing it over 100.
- Therefore, \( 57.12\% = \frac{57.12}{100} \).

2. **Eliminate the Decimal**:
- To eliminate the decimal in the numerator, we can multiply both the numerator and the denominator by 100 (since there are two decimal places).
- This gives us:
\[ \frac{57.12 \times 100}{100 \times 100} = \frac{5712}{10000} \]

3. **Simplify the Fraction**:
- Now, we need to simplify the fraction \( \frac{5712}{10000} \).
- We can find the greatest common divisor (GCD) of 5712 and 10000 to simplify the fraction.
- After performing the GCD calculation, we find that the GCD is 4.
- Dividing both the numerator and denominator by 4:
\[ \frac{5712 \div 4}{10000 \div 4} = \frac{1428}{2500} \]

4. **Further Simplification**:
- We can check if \( \frac{1428}{2500} \) can be simplified further.
- The GCD of 1428 and 2500 is 2, so we divide both by 2:
\[ \frac{1428 \div 2}{2500 \div 2} = \frac{714}{1250} \]

5. **Final Fraction**:
- The simplest form of the fraction equivalent to 57.12% is \( \frac{714}{1250} \).

### Final Answer:
The fractional equivalent of 57.12% is \( \frac{714}{1250} \).

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