Practical examples of comparing astronomical distances in scientific notation

📚 Quick Study Guide

• 🌌 Scientific Notation: A way to express very large or very small numbers using powers of 10. The general form is $a \times 10^b$, where $1 \le |a| < 10$ and $b$ is an integer.
• 📏 Units of Astronomical Distance:
  • Astronomical Unit (AU): The average distance between the Earth and the Sun (approximately $1.5 \times 10^{11}$ meters).
  • Light-Year (ly): The distance light travels in one year (approximately $9.461 \times 10^{15}$ meters).
  • Parsec (pc): Approximately 3.26 light-years (approximately $3.086 \times 10^{16}$ meters).
• ➕ Comparing Distances: To compare distances in scientific notation, ensure they are in the same units. Divide the larger distance by the smaller distance to find the ratio.
• 💡 Example: Comparing the distance to Proxima Centauri (4.24 light-years) to the distance to the Andromeda Galaxy (2.5 million light-years): $\frac{2.5 \times 10^6 \text{ ly}}{4.24 \text{ ly}} \approx 5.9 \times 10^5$. The Andromeda Galaxy is about 590,000 times farther than Proxima Centauri.

Practice Quiz

1. Question 1: The distance to a certain star is $5 \times 10^{16}$ meters. Which unit is most appropriate to represent this distance?
   1. Astronomical Unit (AU)
   2. Kilometer (km)
   3. Light-Year (ly)
   4. Meter (m)
2. Question 2: Which of the following represents 123,000,000 in scientific notation?
   1. $123 \times 10^6$
   2. $1.23 \times 10^8$
   3. $1.23 \times 10^7$
   4. $0.123 \times 10^9$
3. Question 3: The distance to Star A is $3 \times 10^{17}$ meters, and the distance to Star B is $6 \times 10^{16}$ meters. How many times farther is Star A than Star B?
   1. 2 times
   2. 5 times
   3. 20 times
   4. 0.5 times
4. Question 4: What is the approximate distance of 1 parsec in light-years?
   1. 1 light-year
   2. 3.26 light-years
   3. 9.46 light-years
   4. 30.86 light-years
5. Question 5: If the distance from Earth to Mars is approximately $2.25 \times 10^{8}$ km, and the speed of a spacecraft is $5 \times 10^{4}$ km/h, how long will it take the spacecraft to reach Mars (in hours)?
   1. $4.5 \times 10^{3}$ hours
   2. $1.125 \times 10^{13}$ hours
   3. $4.5 \times 10^{12}$ hours
   4. $4.5 \times 10^{2}$ hours
6. Question 6: Which distance is greater: $7.8 \times 10^{9}$ km or $9.1 \times 10^{12}$ m?
   1. $7.8 \times 10^{9}$ km
   2. $9.1 \times 10^{12}$ m
   3. They are equal
   4. Cannot be determined
7. Question 7: Convert 500 light-years into meters using scientific notation. (1 light-year = $9.461 \times 10^{15}$ meters)
   1. $4.7305 \times 10^{17}$ meters
   2. $4.7305 \times 10^{18}$ meters
   3. $4.7305 \times 10^{16}$ meters
   4. $4.7305 \times 10^{15}$ meters