To determine the first seven digits after the decimal point for the repeating decimal [tex]\( 0.\overline{50} \)[/tex], follow these steps:
1. Recognize that [tex]\( 0.\overline{50} \)[/tex] means that the digits "50" repeat indefinitely after the decimal point.
2. Write out the repeating portion to understand the pattern better:
[tex]\[
0.5050505050...
\][/tex]
3. Identify the first seven digits after the decimal point. Starting immediately after the decimal, count the first seven digits:
[tex]\[
5050505
\][/tex]
Therefore, the first seven digits after the decimal point in [tex]\( 0.\overline{50} \)[/tex] are:
[tex]\[
5050505
\][/tex]
