To express the given mass in terms of solar masses and to two significant figures, let's break down the steps:
1. Determine the given mass: The problem appears to deal with a certain mass which is an integer multiple of the sun's mass. Specifically, it looks like we're dealing with 79 times the mass of the sun.
2. Mass of the Sun: The mass of the Sun is given as [tex]\(2.0 \times 10^{30}\)[/tex] kg.
3. Multiplying by the given mass:
- Multiply the solar masses:
[tex]\[
\text{Total Mass} = 79 \times M_{\text{Sun}}
\][/tex]
- Since [tex]\(M_{\text{Sun}} = 2.0 \times 10^{30}\)[/tex] kg:
[tex]\[
\text{Total Mass} = 79 \times 2.0 \times 10^{30} \text{ kg}
\][/tex]
4. Expressing the result:
- Since we need the result in solar masses and only to two significant figures, we express the mass directly:
[tex]\[
\frac{\text{Total Mass}}{M_{\text{Sun}}} = \frac{79 \times 2.0 \times 10^{30}}{2.0 \times 10^{30}} = 79 \text{ solar masses}
\][/tex]
- This simplifies our result to,
[tex]\[
79 \text{ solar masses}
\][/tex]
5. Rounding to two significant figures:
- The number 79 already has two significant figures, so no further rounding is necessary.
Therefore, the final answer is:
[tex]\[
\boxed{79 \text{ solar masses}}
\][/tex]
