To convert the fraction [tex]\(\frac{4}{9}\)[/tex] into its decimal form, we follow a systematic approach:
1. Understanding the Fraction:
- The fraction [tex]\(\frac{4}{9}\)[/tex] consists of a numerator (4) and a denominator (9). This means we need to divide 4 by 9 to determine its decimal equivalent.
2. Performing the Division:
- We execute the division of the numerator by the denominator, which is [tex]\(4 \div 9\)[/tex].
- If we divide 4 by 9, we get a repeating decimal.
3. Obtaining the Decimal Equivalent:
- When you divide 4 by 9, the result is approximately 0.4444444444444444.
- This result indicates that the digit 4 repeats indefinitely.
4. Representation of the Repeating Decimal:
- The repeating decimal can be denoted compactly as [tex]\(0.\overline{4}\)[/tex]. This notation indicates that the digit "4" repeats endlessly.
Therefore, the fraction [tex]\(\frac{4}{9}\)[/tex] in decimal form is approximately [tex]\(0.444\ldots\)[/tex], where the digit "4" repeats indefinitely.
