Given the problem [tex]\(2.8 + 7 . \overline{2} =\)[/tex]:
1. First, let's understand what [tex]\(7 . \overline{2}\)[/tex] represents. This is a repeating decimal where the digit 2 repeats indefinitely. So, [tex]\(7 . \overline{2} = 7.222222 \ldots \)[/tex].
2. Now we need to add [tex]\(2.8\)[/tex] and [tex]\(7.222222 \ldots\)[/tex].
3. To add these numbers, align the decimal points:
[tex]\[
\begin{array}{r}
2.8 \\
+ \, 7.222222 \ldots \\
\hline
\end{array}
\][/tex]
4. Perform the addition as follows:
- Start by adding the tenths place:
- [tex]\(8 + 2 = 10\)[/tex] (write down 0, carry over 1)
- Now add the units place, including the carry-over:
- [tex]\(2 + 7 + 1 = 10\)[/tex] (write down 0, carry over 1)
- The result is written as [tex]\(10.022222 \ldots\)[/tex]
So, the final result is [tex]\(10 . \overline{2} = 10.022222 \ldots\)[/tex].
Therefore, the sum of [tex]\(2.8 + 7 . \overline{2}\)[/tex] is:
[tex]\[
2.8 + 7 . \overline{2} = 10.022222 \ldots
\][/tex]
