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Drag the tiles to the boxes to form correct pairs.

The table shows the distances between a star and three celestial objects. Use the conversion factors to rewrite the distances in different, but equivalent, units.

\begin{tabular}{|l|l|}
\hline
Celestial Objects & Distance from the Star \\
\hline
Object A & 0.000001877 pc \\
\hline
Object B & 30.06 AU \\
\hline
Object C & 778.3 million km \\
\hline
\end{tabular}

Conversion factors:
[tex]\[
1 \text{ AU } = 1.5 \times 10^8 \text{ km}
\][/tex]
[tex]\[
1 \text{ light-year } = 9.5 \times 10^{12} \text{ km}
\][/tex]
[tex]\[
1 \text{ parsec } = 31 \text{ trillion km } , \text{ or about } 3.262 \text{ light-years}
\][/tex]

Distance to Object A:
Distance to Object B:
Distance to Object C:

Sagot :

GinnyAnsweridn
To solve this problem, let’s use the given conversion factors to convert the distances for each celestial object into different, but equivalent, units.

### Step-by-step Solution:

Distance to object A:

Given:
- Distance in parsecs (pc): 0.000001877 pc

Conversion factor:
- 1 parsec = 31 trillion kilometers (31 \times 10^{12} km)
- 1 parsec ≈ 3.262 light-years (ly)

Using the conversion factor to convert parsecs to kilometers:
- Distance in kilometers = 0.000001877 pc \times 31 \times 10^{12} km/pc
- Distance in kilometers = 58,187,000.0 km

Using the conversion factor to convert parsecs to light-years:
- Distance in light-years = 0.000001877 pc \times 3.262 ly/pc
- Distance in light-years = 6.122774e-06 ly

So the distances to object A are:
- 58,187,000.0 km
- 6.122774e-06 ly

Distance to object B:

Given:
- Distance in Astronomical Units (AU): 30.06 AU

Conversion factor:
- 1 AU = 1.5 \times 10^8 km

Using the conversion factor to convert AU to kilometers:
- Distance in kilometers = 30.06 AU \times 1.5 \times 10^8 km/AU
- Distance in kilometers = 4,509,000,000.0 km

So the distance to object B is:
- 4,509,000,000.0 km

Distance to object C:

Given:
- Distance in kilometers (km): 778.3 million km, which is 778.3 \times 10^6 km

Conversion factor:
- 1 light-year = 9.5 \times 10^{12} km

Using the conversion factor to convert kilometers to light-years:
- Distance in light-years = 778.3 \times 10^6 km / 9.5 \times 10^{12} km/ly
- Distance in light-years = 8.192631578947369e-05 ly

So the distance to object C is:
- 8.192631578947369e-05 ly

### Pairing Distances to Celestial Objects:

- Distance to object A:
- 58,187,000.0 km
- 6.122774e-06 ly

- Distance to object B:
- 4,509,000,000.0 km

- Distance to object C:
- 8.192631578947369e-05 ly

Hence, we can summarize the pairs as follows:

- Object A: 58,187,000.0 km, 6.122774e-06 ly
- Object B: 4,509,000,000.0 km
- Object C: 8.192631578947369e-05 ly
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