Name ______________________________
Date ___________
Scientific Notation Problems and SOLUTIONS
No Calculators for Problems 1-5
1.
(6  106 )(2  103 )(2  103 )
(4  104 )

( 6 x2 x2 )( 10 6 x103 x103 )  24  10 633 
  6 x108
  
4
4
4 x10 4
10
 

(4  106 )(2  103 )
63
10 9
 4 x 2  10 


 5 x108
2.
 4 4   0.5 x

4
4
1
(8  10 )(2  10 )  8 x2  10

3.
4.
5.
(5  106 )(2  103 )(3  103 )
(5  104 )
(7  106 )(2  103 )(5  103 )
(2  104 )
(4  106 )(5  103 )
(8  104 )(5  103 )
 2 x3  10

4
 1  10

6  3 3
 7 x5  10


4
 1  10
6  3 3

1012
  6 x 4  6 x10124  6 x108
10


1012
  35x 4  35x10124  35x108  3.5 x109
10

6 3
10 3
 4  10 


0
.
5
x
 0.5 x10 3( 1)  0.5 x10 4  5 x10 3
 43 
1
8
10
10
 

  
6. Using the following data:
the volume of a sphere = (4/3) (pi)R 3
Radius of the earth= 6.3×106 m.
Mass of earth= 5.9742 × 10 24 kg
a) Find the density of the earth in kg/m 3 (Note: this method will only yield an approximate value for the
density of the earth).
Looking at the units of the density you are asked to find (kg/m3), you need to divide the mass of the earth
(in kg) by the volume of the earth (in m3). The mass of the Earth is given. The volume of the Earth can
be calculated using the given formula:
VE  (4 / 3)RE3  (4 / 3) (6.3x10 6 m) 3  (4 / 3) (6.33 )(10 6 ) 3 m 3  1046 .9 x10 18 m 3
IMPORTANT: Notice that I have not rounded the answer yet. Since it is an intermediate step, not the final
answer, leave in lots of figures. Do not round to appropriate sig figs until the final answer otherwise you
may get rounding errors.
 M (kg )   5.974 x10 24 (kg )   5.974  10 24  kg 
2418

densityE   E 3   
kg / m 3
 18  3   0.0057 x10
18
3 
 VE (m )   1046.9 x10 (m )   1046.9  10  m 
 0.0057 x106  5.7 x103 kg / m 3
b) Express Earth’s density in g/cm3
kg 1000 g  1m 
x
x

m3
1kg  100cm 
kg 103 g
1m 3
 5.7 x103 3 x
x
m
1kg 1003 cm3
3
densityE  5.7 x103

5.7 x106 g
 5.7 g / cm3
6
3
10
cm
7. What is the ratio of Milky Way radius to our solar system radius given that, the distance from pluto to sun
is 5.9×10 12 meters and the Milky Way disk radius is. 3.9×1020 meters. Round the coefficient to the
nearest tenth.
rMilkyWay  3.9 x10 20   3.9  10 20 
2012

 
 0.66 x108  6.6 x10 7
 12   0.66 x10
12 
rSolarSys  5.9 x10   5.9  10 
8. The speed of light is 3 x 10 8 meters/second. If the sun is 1.5x 1011 meters from earth, how many seconds
does it take light to reach the earth? Express your answer in scientific notation.
 1.5 x1011 (m) 
 
3 x10 8 m / s  
t ( s)


11
 1.5 x10 m   1.5  1011  m 
118
3
  
t ( s )  
 8 
  0.5 x10 s  0.5 x10  500s  8.3 min
8
 3 x10 m / s   3  10  m / s 