Download Large and Small Numbers: Scientific Notation

Large and Small Numbers: Scientific Notation Solutions
*** Please note with these solutions if your answer is not exactly the same as I
have, in a test/hw/quiz situation you would loose marks for incorrect sig figs ***
1.
Convert the following measured quantities from ordinary notation to scientific
notation
Mean wavelength of sodium light
Speed of light in a vacuum
Half-life of Uranium-235
Atomic mass unit
Avogadro’s number
Melting point of Tungsten
2.
Ordinary notation
0.000 000 5893 meters
299 793 000 m/s
710 000 000 years
0.000 000 000 000 000
000 000 001 660 531 g
602 300 000 000 000 000
000 000
3410oC
Scientific Notation
5.893 x 10 -7 m
2.99793 x 108 m/s
7.1 x 108 yrs
1.660531 x 1024 g
6.023 x1023
3.41 x 103 oC
Convert each of the following measured quantities form scientific notation to ordinary
notation
Mass of an election
Temperature at which atomic fusion
occurs
Lowest possible temperature
Diameter of the Andromeda Galaxy
Radius of a hydrogen energy level
Charge of a proton
Scientific Notation
9.109 x 10-31 kg
1.5 x 107 oC
2.73 x 102 oC
1.9 x 1015 km
5.3 x 10-11 m
1.6 x 10-19 coulomb
Ordinary notation
0.000 000 000 000 000 000
000 000 000 000 9109 kg
15 000 000oC
273 oC
1 900 000 000 000 000 km
0.000 000 000 053 m
0.000 000 000 000 000 000
16C
3.
Express each of the following numbers in scientific notation
a. 2370
2.37 x 103
b. 0.03
3 x 10-2
c. 0.000 000 000 000 274
2.74 x 10-13
d. 985 000 000 000 000 000 000
9.85 x 1020
e. 15.045
1.5045 x 10-1
f. 6003
6.003 x 103
g. 0.000 045
4.5 x 10-5
h. 0.000 000 007 07
7.07 x 10-9
4.
Express each of the following in ordinary notation
a. 5.63 x 10-3
0.005 63
b. 6.7 x 105
670 000
c. 1.01 x 103
1010
d. 9.899 x 10-8
0.000 000 098 99
e. 2 x 106
2 000 000
f. 7.85 x 10-2
0.0785
g. 3.444 x 1010
34 440 000 000
h. 2.0002 x 10-4
0.000 20002
1
5.
6.
Perform the indicated operations
a. 103 x 106 =
b. 10-2 x 105 =
c. 107 =
103
d. 102 =
108
e. 102 =
10-5
f. 10-1 x 1010 =
109
103
104
10-6
107
109
Perform the indicated operations. Convert all the answers to scientific notation,
showing the correct number of significant digits
a. (5.4 x 102 ) (2.5 x 109) =
13.5 x 1011 = 1.4 x 1012
-5
6
b. (1.2 x 10 ) (5.4 x 10 ) =
6.5 x 101
-7
-7
c. (3.3 x 10 ) (6.6 x 10 ) =
21.78 x 10-14 = 2.2 x 10 -13
3
-1
d. (2.56 x 10 ) (1.00 x 10 ) =
2.56 x 102
12
e. 7.25 (5.5 x 10 ) =
4.00 x 1012
7
f. (1.5 x 10 ) =
0.33 x 102 = 3.3 x 101
5
(4.5 x 10 )
g. (9.6 x 102) =
3.0 x 10-6
8
(3.2 x 10 )
h. (8.05 x 10-9) =
1.61 x 10-5 = 2 x 10-5
-4
(5 x 10 )
i.
4.5
=
3.3 x 103
-3
(1.38 x 10 )
j. (2.75 x 106) =
9.8 x 105
2.5
k. (3.2 x 105) + (4.5 x 105) =
7.7 X 105
-3
-3
l. (9.2 x 10 ) – (5.6 x 10 ) =
3.6 X 10-3
2
-5
m. (4.33 x 10 ) + (8.3 x 10 ) =
4.33 X 102
-6
-5
-5
n. (6.81 x 10 ) – (8.3 x 10 ) = 0.681x10 – 8.3 x 10-5= -7.6 X10-5 *
o. (5.8 x 104) – (6.42 x 104) =
-6.2 x 103
7
8
7
p. (2.75 x 10 ) + (5.5 x 10 ) = 57.75 x 10 = 5.8 x 108
q. (1.9 x 10-3) – (1.5 x 10-4) = 17.4 x 10-4 = 1.7 x 10-3
r. (4.3 x 104) – (8.5 x 103) = 4.3x104 + 0.85x104 = 5.2x104
*
s. (8.7 x 103) + (7.9 x 102) = 8.7 x 103 + 0.79 x 103 = 9.5 x 103
*
t. (6.25 x 104) – (3.5 x 103) = 6.25 x 104 – 0.35 x 104 = 5.90 x 104
*
* for these question I convert to the same exponent, or expand completely so I
can line up each column and round my significant digits to the least precise
measurement
2