To convert the fraction [tex]\(\frac{2}{11}\)[/tex] into a decimal form, we can follow these steps:
1. Perform the Division:
- When we divide 2 by 11, we get a repeating decimal. The long division of 2 by 11 results in the decimal [tex]\(0.181818181818...\)[/tex].
2. Identify the Repeating Block:
- In the decimal [tex]\(0.181818181818...\)[/tex], you will notice that the digits "18" repeat indefinitely. This is known as a recurring or repeating decimal.
3. Express the Recurring Decimal using Dot Notation:
- In dot notation, we place a dot above the repeating digits to indicate that they repeat forever.
- For the decimal [tex]\(0.181818181818...\)[/tex], the repeating block is '18', and we write it in dot notation as [tex]\(0.\overline{18}\)[/tex].
Thus, the fraction [tex]\(\frac{2}{11}\)[/tex] written as a recurring decimal using dot notation is [tex]\(0.\dot{1}\dot{8}\)[/tex].
