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Step 1:I'll solve this step-by-step, carefully following the LaTeX formatting guidelines:
Step 2:: Understand the Conversion
To convert a decimal to a fraction, we need to: - Identify the decimal's value - Find an equivalent fraction in simplified form
Step 3:: Analyze the Decimal
The decimal is $$0.3125
Step 4:: Determine the Denominator
- This means we'll start with a denominator of $$10^{4} = 10000
- Count the number of decimal places (4 in this case)
Step 5:: Convert to Fraction
0.3125 \times 10000 = 3125
- Multiply the decimal by the denominator
Step 6:: Simplify the Fraction
- The initial fraction is $$\frac{3125}{10000}
- We can simplify this by dividing both numerator and denominator by their greatest common factor
Step 7:: Reduce the Fraction
\frac{3125 \div 625}{10000 \div 625} = \frac{5}{16}
- Divide both 3125 and 10000 by 625
Final Answer
0.3125 = \frac{5}{16}
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