ASTR1101

REVIEW

Scientific Notation is used a lot in astronomy. It helps us to write succinctly the very large and small numbers we often encounter (sizes, distances, times, etc).

Exercise 1: Express the following numbers without a power of ten:
1) 10⁴ =
2) 10⁷ =
3) 10^0.5 =
4) 10^-1 =
5) 10^-4 =
6) 10^-3.5 =

Exercise 2: Express the following numbers as powers of ten.

7) 10
8) 100,000
9) 1,000,000,000,000,000,000
10) 0.001
11) 1
12) 0.000000001 

Exercise 3: Convert the following numbers to Scientific Notation:

14) 5,213 =
15) 73,200 =
16) 23.21 =

17) 21,000,000,000 =
18) 4,713,000,000 =

19) 0.02 =
20) 0.000314 =
21) 0.00000000043791

Exercise 4: Convert the following numbers to decimal notation:

22) 2 x 10³ =
23) 2.331 x 10⁵ =
24) 9.51 x 10²² =

25) 5 x 10^-3 =
26) 7.6278 x 10^-5 =
27) 10³ + 10⁵ =

28) (2.51 x 10² ) + (5.23 x 10⁴ ) =
29) 10⁴ - 10² =

30) (2 x 10⁴ ) - (7 x 10² ) =
31) 10¹² x 10⁵ =

32) (7.2 x 10⁵ ) x (2.12 x 10^-2 ) =
33) 10⁹ / 10⁴ =

34) (2.3 x 10⁷) / (9.2 x 10²) =

ANSWERS:  

1) 10,000 
2) 10,000,000 
3) sqrt(10)  
4) 0.1

5) 0.0001 
6) 1/sqrt(10000000)

7) 10¹        
8) 10⁵   
9) 10¹⁸    
10) 10^-3    
11) 10⁰    
12) 10^-9 

14) 5.213 x 10³ 
15) 7.32 x 10⁴ 
 16) 2.321 x 10¹ 
17) 2.1 x 10¹⁰

18) 4.713 x 10⁹ 
19) 2 x 10^-2 
20) 3.14 x 10^-4 
 21) 4.3791 x 10^-10 

22) 2,000

23) 233,100 
24) 95,100,000,000,000,000,000,000 
25) 0.005 
26) 0.000076278

27) 1,000 +100,000 = 101,000 
28) 251 + 52,300 = 52,551

29) 10,000 - 100 = 9,900 
30) 20,000 - 700 =19,300

31) 10⁽¹²⁺⁵⁾ = 10¹⁷ = 100,000,000,000,000,000 
32) (7.2 x 2.12) x 10^(5-2) = 15.264 x 10³ = 15,264

33) 10^(9-4) = 10⁵ = 100,000 
34) (2.3 / 9.2) x 10^(7-2) = (0.25) x 10⁵ = 25,000


CHAPTER 1