To solve the problem of finding the product of [tex]\(2.5\)[/tex] and [tex]\(0.\overline{3}\)[/tex] and expressing the result as a decimal with four decimal places, follow these steps:
1. Understand the given values:
- [tex]\(2.5\)[/tex] is already in decimal form.
- [tex]\(0.\overline{3}\)[/tex] represents the repeating decimal [tex]\(0.3333...\)[/tex].
2. Calculation:
- Multiply [tex]\(2.5\)[/tex] by [tex]\(0.3333\)[/tex]:
[tex]\[
2.5 \cdot 0.3333 = 0.8332499999999999
\][/tex]
Here, [tex]\(0.8332499999999999\)[/tex] is the product obtained from the multiplication.
3. Round the product:
- We need to round the result to four decimal places. To do this, follow standard rounding rules:
[tex]\[
0.8332499999999999 \approx 0.8332
\][/tex]
Thus, the product of [tex]\(2.5\)[/tex] and [tex]\(0.\overline{3}\)[/tex] rounded to four decimal places is:
[tex]\[
\boxed{0.8332}
\][/tex]
