1. Astronomical Numbers SNC1D

2. Powers of Ten Numbers in astronomy are often much larger than we are used to dealing with in daily life. We often express them in terms of powers of ten. Example:1 000 000 000 = 10 9

3. Powers of Ten http://www.youtube.com/watch?v=0fKBhvDjuy0

4. Scientific Notation Scientific notation may be used to write numbers in terms of powers of ten. Example: This coefficient must have an absolute value between 1 and 10. All significant digits must be shown.

5. Large Numbers To write a large number in scientific notation, count how many places to the left you have to move the decimal until it is after the first non-zero. This is your power of ten.

6. Small Numbers For small numbers, you count places to the right. This is your negative power of ten.

7. Practice Write each of the following in scientific notation: 43800 = 0.050 = 7100000000 = 0.00088 = 10.1 =

8. Practice Write each of the following in scientific notation: 43800 = 4.38 x 10 4 0.050 = 7100000000 = 0.00088 = 10.1 =

9. Practice Write each of the following in scientific notation: 43800 = 4.38 x 10 4 0.050 = 5.0 x 10 -2 7100000000 = 0.00088 = 10.1 =

10. Practice Write each of the following in scientific notation: 43800 = 4.38 x 10 4 0.050 = 5.0 x 10 -2 7100000000 = 7.1 x 10 9 0.00088 = 10.1 =

11. Practice Write each of the following in scientific notation: 43800 = 4.38 x 10 4 0.050 = 5.0 x 10 -2 7100000000 = 7.1 x 10 9 0.00088 = 8.8 x 10 -4 10.1 =

12. Practice Write each of the following in scientific notation: 43800 = 4.38 x 10 4 0.050 = 5.0 x 10 -2 7100000000 = 7.1 x 10 9 0.00088 = 8.8 x 10 -4 10.1 = 1.01 x 10 1

13. You can go from scientific to standard notation by simply moving the decimal back....

14. More Practice Write each of the following in standard notation: 5.1 x 10 3 = 8.2 x 10 -3 = 3.00 x 10 6 = 4.0 x 10 -5 = 5.75 x 10 -1 =

15. More Practice Write each of the following in standard notation: 5.1 x 10 3 = 5100 8.2 x 10 -3 = 3.00 x 10 6 = 4.0 x 10 -5 = 5.75 x 10 -1 =

16. More Practice Write each of the following in standard notation: 5.1 x 10 3 = 5100 8.2 x 10 -3 = 0.0082 3.00 x 10 6 = 4.0 x 10 -5 = 5.75 x 10 -1 =

17. More Practice Write each of the following in standard notation: 5.1 x 10 3 = 5100 8.2 x 10 -3 = 0.0082 3.00 x 10 6 = 3000000 4.0 x 10 -5 = 5.75 x 10 -1 =

18. More Practice Write each of the following in standard notation: 5.1 x 10 3 = 5100 8.2 x 10 -3 = 0.0082 3.00 x 10 6 = 3000000 4.0 x 10 -5 = 0.000040 5.75 x 10 -1 =

19. More Practice Write each of the following in standard notation: 5.1 x 10 3 = 5100 8.2 x 10 -3 = 0.0082 3.00 x 10 6 = 3000000 4.0 x 10 -5 = 0.000040 5.75 x 10 -1 = 0.575

20. But you don’t have to change to standard notation to enter the number into your calculator....

21. Using Your Calculator

22. Practice Try: (5.0 x 10 3 )(6.2 x 10 11 )

23. Practice Try: (5.0 x 10 3 )(6.2 x 10 11 ) Answer: 3.1 x 10 15

24. More Practice Try: 6.4 x 10 15 4.0 x 10 -4

25. More Practice Try: 6.4 x 10 15 4.0 x 10 -4 Answer: 1.6 x 10 19

26. Other Units Sometimes astronomical numbers are given with reference to a standard. Example: 1 Solar Mass = 1.99 x 10 30 kg The star Rigel has a mass of 3.58 x 10 31 kg or 18 Solar Masses.

27. Astronomical Units Distances in the solar system are often even in Astronomical Units (AU). 1 AU is the distance from the Earth to the Sun. = 1.50 x 10 11 m

28. Astronomical Units What is the distance from Mars to the Sun in m?

29. Astronomical Units What is the distance from Mars to the Sun in m? 1.52(1.50 x 10 11 m) = 2.28 x 10 11 m

30. Light Years Distances outside the solar system are often given in light years. 1 light year is the distance light travels in a year = 9.46 x 10 15 m

31. Addendum To convert km to m, add 3 to the exponent. (Remember that 10 3 = 1000.) 1.50 x 10 8 km = 1.50 x 10 11 m (To convert m to km, subtract 3 from the exponent.)