Sure, let's solve this step-by-step.
1. Understanding the Problem: We need to convert a volume given in cubic yards to cubic meters. Specifically, we need to convert [tex]\(2.9 \, \text{yd}^3\)[/tex] to cubic meters ([tex]\(\text{m}^3\)[/tex]).
2. Conversion Factor: We know that [tex]\(1\)[/tex] cubic yard is equivalent to approximately [tex]\(0.764554857984\)[/tex] cubic meters. This conversion factor helps us to transition between the two units.
3. Setting Up the Conversion: To find out how many cubic meters are in [tex]\(2.9 \, \text{yd}^3\)[/tex], we need to multiply [tex]\(2.9\)[/tex] by the conversion factor [tex]\(0.764554857984\)[/tex].
4. Calculation:
[tex]\[
2.9 \, \text{yd}^3 \times 0.764554857984 \, \frac{\text{m}^3}{\text{yd}^3} \approx 2.2172090881536 \, \text{m}^3
\][/tex]
5. Result: Therefore, [tex]\(2.9 \, \text{yd}^3 \approx 2.2172090881536 \, \text{m}^3\)[/tex].
So, to conclude:
[tex]\(\boxed{2.2172090881536 \, \text{m}^3}\)[/tex]
