express 5.65 as decimal as a percentage and as a reduced fraction

To express \(5.65\) as a decimal, percentage, and reduced fraction, we proceed as follows:

1. **Decimal**: The decimal representation is simply \(5.65\) itself.

2. **Percentage**: To convert \(5.65\) to a percentage, multiply by \(100\):
   \[
   5.65 \times 100 = 565\%
   \]
   So, \(5.65\) as a percentage is \(565\%\).

3. **Reduced Fraction**: Convert \(5.65\) to a fraction by recognizing that \(5.65\) is the same as \( \frac{565}{100}\). Now, reduce this fraction:

   - Find the greatest common divisor (GCD) of \(565\) and \(100\), which is \(5\).
   - Divide the numerator and denominator by \(5\):
     \[
     \frac{565 \div 5}{100 \div 5} = \frac{113}{20}
     \]

   Therefore, the reduced fraction form of \(5.65\) is \(\frac{113}{20}\).

### Summary:
- **Decimal**: \(5.65\)
- **Percentage**: \(565\%\)
- **Reduced Fraction**: \(\frac{113}{20}\)

Would you like more details or have any questions?

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Here are some related questions you might explore:
1. How would you convert a repeating decimal like \(5.\overline{6}\) into a fraction?
2. How do you reduce fractions to their simplest form?
3. How would you express \(0.0565\) as a percentage?
4. What steps are involved in converting a decimal into a fraction?
5. How would you convert a percentage greater than 100% to a decimal?

**Tip**: To convert any decimal to a percentage, simply multiply by 100 and add the "%" symbol.

Express 5.65 as decimal as a percentage and as a reduced fraction.

Understand how to express 5.65 as a decimal, convert it to a percentage (565%), and reduce it to the simplest fraction (113/20). This step-by-step solution explores decimal, percentage, and fraction reduction concepts. Suitable for students in Grades 6-8.

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