To find the next three numbers of the repeating decimal produced by the fraction [tex]\(\frac{7}{9}\)[/tex], let's break down the steps:
1. Understand the fraction:
- The fraction [tex]\(\frac{7}{9}\)[/tex] simplifies to a repeating decimal.
2. Convert the fraction to decimal form:
- When you divide 7 by 9, it yields a decimal that repeats. The repeating decimal form of [tex]\(\frac{7}{9}\)[/tex] is [tex]\(0.\overline{7}\)[/tex], which means 0.777777...
3. Identify the repeating part:
- The repeating decimal here is "777777..." where the digit '7' repeats indefinitely.
4. Determine the next three numbers:
- Since the repeating pattern is '7', the next three numbers in the sequence, following the pattern, would just continue the same.
Therefore, the next three numbers of the repeating decimal produced by the fraction [tex]\(\frac{7}{9}\)[/tex] are:
[tex]\[
777
\][/tex]
