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.