Problem Set 1.1:        Math Review: Scientific Notation, Sig. Figs., Units

 

 

Scientific Notation

 

1.     Write the following numbers in scientific notation:

 

a) 5 500 000 000         5.5 x 109                                  b) 78 023 010 000                   7.802301 x 1010

 

c)  0.091                      9.1 x 10-2                                 d)  0.000 003 004                    3.004 x 10-6

 

2.     Write the following numbers in regular notation:

 

a)  5.5 x 10-7                0.000 000 000 55                                b)  7.1 x 1010               71 000 000 000

 

c)  1.0 x 103                 1000                            d)  6.02  x 1023                              6 02 000 000 000 000 000 000 000

 

3.     Compute the following:

 

a)  103 x 105                1.0 x 108                                  b)  4 x 10-3 x -5 x 10-5             -2 x 10-7

 

c)  10-3 x 105               1.0 x 102                                  d)  (8.0 x 105)(1.2 x 108)         9.6 x 1013

 

e)  103 ü 105                1.0 x 10-2                                 f)  2.3 x 10-3 ü 1.0 x 10-5        230

 

g)  10-3 ü 105               1.0 x 10-8                                 h)  (8.0 x 105) ü (1.2 x 108)    6.67 x 10-3

 

i)  (3 x 108)2                9 x 1016                                   j)                              2 x 104

 

4.     The mass of an electron is 9.1 x 10-31 kg.  What is the mass of 3.2 x 103 electrons?

5.     The velocity of light is 3.0 x 108 m/s.  How long does it take light to travel to the moon?  (The distance from the earth to the moon is 3.84 x 108 m.) Give your answer in seconds and in minutes.

6.     Find the area of a rectangle that is 1.5 x 103 cm by 6.8 x 104 cm.

7.     Find the area of a circle that is 7.5 x 104 cm in diameter.

Significant Figures

 

1.  How many significant figures are in the following numbers?

 

a)  425                         3                                  b)  1.2                          2

 

c)  25.2                        3                                  d)  6.3706                    5

 

e)  8.11002                  6                                  f)  2500                       2

 

g)  450,000                  2                                  h)  5080.                      4

 

i)  0.00897                   3                                  j)  0.1000                     4

 

k)  7.01 x 103              3                                  l)  7.00 x 10-4              3

 

m)  0.0089700             5

 

2.  Compute the following - use significant figures.

 

a)  6.3 + 10.764 + 4.56           21.6                 b)  3.72 ü 2.1              1.8

 

c)   67.98 + 8 + 43.2               119                  d)  56  x  3.21              1.8 x 102

 

Unit Conversions

 

1.     Convert the followingÉ

 

a)  5 kg =               5000 g                                                 b)  8765 m =               8.765 km        

                 

c)  560 g =             0.56 kg                                                d)  25 km =                 25 000 m

 

e)  59.2 minutes =             3552 seconds                          f)  87 seconds =          1.45 minutes

 

g)  25 km/h =                    6.94 m/s                                  h)  120 m/s =               432 km/h

 

2.     Convert the followingÉ

 

a)  37 metres =                  3700 cm                                  b)  7 metre =                7000 millimetres

 

c)  47 cm =                        470 mm                                   d) 47 cm =                   0.47 m

 

e)  5.0 hm =                       50 000 cm                               f)  18 km =                  1.8 x 106 cm

 

g) 18 hm =                        1.8 km

 

3.     a)  How many minutes are in a year?

b)  How long (in hours) will it take you to count to a billion counting one number every second?