unit conversion

Question

One astronomical unit (AU) is approximately 1.496 × 10⁸ km. If the distance from Earth to a star is 4.22 light years, what is this distance in astronomical units? (1 light year = 9.46 × 10¹² km)

RankGuru · Accepted Answer

1. **Calculate Distance in km**:
   - $D = 4.22 	ext{ LY} 	imes 9.46 	imes 10^{12} 	ext{ km/LY} \approx 39.921 	imes 10^{12}$ km.
2. **Convert to AU**:
   - $D_{	ext{AU}} = \frac{	ext{Total distance in km}}{	ext{Value of 1 AU in km}}$.
   - $D_{	ext{AU}} = \frac{39.921 	imes 10^{12}}{1.496 	imes 10^8}$.
3. **Calculation**:
   - $D_{	ext{AU}} = 26.685 	imes 10^4 = 2.6685 	imes 10^5$ AU.
4. **Final Value**: Rounding to appropriate significance gives **$2.67 	imes 10^5$ AU**.

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