Decimal and fraction conversion is a simple way to represent numbers in different forms. Here’s how you can do it:

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1. Decimal to Fraction:

1. Write the Decimal as a Fraction:

   • Place the decimal number over 1. For example, $0.75$ becomes $\frac{0.75}{1}$.

2. Remove the Decimal Point:

   • Multiply the numerator and the denominator by $10^n$, where $n$ is the number of decimal places.
     For $0.75$:
     $\frac{0.75}{1} \times \frac{100}{100} = \frac{75}{100}$.

3. Simplify the Fraction:

   • Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).
     $\frac{75}{100}$ simplifies to $\frac{3}{4}$ (divide both by 25).

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2. Fraction to Decimal:

1. Divide the Numerator by the Denominator:

   • Simply perform the division to convert the fraction into a decimal.
     For $\frac{3}{4}$:
     $3 \div 4 = 0.75$.

2. Recurring Decimals:

   • If the division doesn’t stop (e.g., $\frac{1}{3} = 0.333...$), the decimal is recurring. You can represent it with a bar over the repeating part: $0.\overline{3}$.

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Key Tips:

• Exact Decimals: Some fractions convert into exact decimals (like $\frac{1}{2} = 0.5$).
• Repeating Decimals: Others might repeat endlessly (like $\frac{1}{3} = 0.333...$).

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Would you like to see worked examples? Or do you have any questions?

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5 Related Questions:

1. How do you simplify fractions efficiently?
2. What are terminating and recurring decimals?
3. Can every decimal be converted into a fraction?
4. How do mixed numbers fit into decimal conversions?
5. Why do some fractions produce repeating decimals?

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Tip:

Always reduce fractions to their simplest form for clarity!