how do we change decimals to fractions and fractions to decimals

Converting between decimals and fractions is a fundamental mathematical skill. Here's a step-by-step guide on how to do both:

### 1. Converting a Decimal to a Fraction

#### **Step 1: Write the Decimal as a Fraction**
- Place the decimal over 1. For example, if you have the decimal 0.75:
  
  \[
  0.75 = \frac{0.75}{1}
  \]

#### **Step 2: Eliminate the Decimal**
- Multiply both the numerator (top) and the denominator (bottom) by 10 for every digit after the decimal point. 
  - For 0.75, there are two digits after the decimal, so multiply by 100:
  
  \[
  \frac{0.75 \times 100}{1 \times 100} = \frac{75}{100}
  \]

#### **Step 3: Simplify the Fraction**
- Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  - For \(\frac{75}{100}\), the GCD of 75 and 100 is 25:
  
  \[
  \frac{75 \div 25}{100 \div 25} = \frac{3}{4}
  \]

So, \(0.75\) as a fraction is \(\frac{3}{4}\).

### 2. Converting a Fraction to a Decimal

#### **Step 1: Divide the Numerator by the Denominator**
- Simply divide the numerator by the denominator.
  - For the fraction \(\frac{3}{4}\), divide 3 by 4:
  
  \[
  3 \div 4 = 0.75
  \]

So, \(\frac{3}{4}\) as a decimal is \(0.75\).

### Summary of Methods

- **Decimal to Fraction**: 
  1. Write the decimal over 1.
  2. Multiply both top and bottom to eliminate the decimal.
  3. Simplify the resulting fraction.

- **Fraction to Decimal**:
  1. Divide the numerator by the denominator.

Would you like more details or have any questions about these conversions?

### Related Questions:
1. How do you convert a repeating decimal to a fraction?
2. What is the fraction representation of 0.333... (repeating)?
3. How can you convert a mixed number to a decimal?
4. How do you simplify fractions when the numerator and denominator are large numbers?
5. What is the decimal equivalent of \(\frac{7}{8}\)?

### Tip:
When converting fractions to decimals, if you encounter a repeating decimal, use a bar over the repeating digits to indicate that the pattern continues infinitely.

Learn how to convert decimals to fractions and fractions to decimals with a detailed step-by-step guide. This guide covers fundamental mathematical skills, including decimal representation as fractions and vice versa. Suitable for students in Grades 5-8.

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