Name ___________________________________ Date ______________________ Class ______________________
Chapter 10 – Chemical Quantities
Scientific Notation
Scientific notation is a way to write very large numbers or very small numbers, usually ones with lots of zeros. For
example the number 0.000000000000000000000000000265 is a very small number and the number
8910000000000000000000 is a very large number. To use these number more easily scientists have developed scientific
notation. In scientific notation there is a number called a coefficient then the multiply sign followed by the 10 to a
power.
22
1.34 x 10
Writing Numbers in Standard Notation:
Something to know is that if the power is positive the decimal place is moved to the right as many spaces as the
coefficient, possibly putting zeros in any blank moves. The opposite is true for negative powers, this is called standard
notation.
Write the following numbers in standard notation:
1.) 1.0 x 10-2
2.) 5.8 x 10-4
3.) 2.8 x 10-4
4.) 4.67 x 108
5.) 9.8 x 103
6.) 6.382 x 10-3
7.) 3.5 x 10-6
8.) 7.8 x 10-10
9.) 5.51 x 107
10.) 1.19 x 102
11.) 8.2 x 104
12.) 9.8 x 106
Writing Numbers in Scientific Notation:
Writing numbers in scientific notation is the opposite of writing them in standard notation. If the number is large (zeros
at the end) then the power will be positive. If the number is small (zeros at the beginning) then the power will be
negative. Your power will be the same as the number of spaces you move the decimal to write the coefficient correctly.
In order to write numbers in scientific notation understand that the coefficient is never less than zero and never greater
than 9. In other words the coefficient is always 1-9.
Write the following numbers in scientific notation:
1.) 2000000
2.) 2950000
3.) 841
4.) 0.0923
5.) 0.000443
6.) 241000000
7.) 0.0000710
8.) 50310000
9.) 6290
10.) 7630000
11.) 0.000911
12.) 5300
13.) 73000000
14.) 600
15.) 246.0
16.) 69845869
17.) 0.64278
18.) 547.85
19.) 0.00572
20.) 0.0000006243
21.) 0.78500
Multiplying Numbers in Scientific Notation:
When you multiply numbers in scientific notation you first multiply the coefficients then add the powers. After that you
make sure you have the coefficient written in proper format. If you move the decimal  you increase the power by
how many spaces you moved the decimal. If you move  the decimal you decrease the power by how many spaces you
moved the decimal.
14
-23
(2.35x10 ) x (3.25x10 )
Multiply the following numbers:
1.) (1.2 x 103) X (5.7 x 104)
2.) (3.78 x 100) X (6.79 x 103)
3.) (8.74 x 104) X (9.1 x 105)
4.) (4.21 x 103) X (5.0 x 104)
5.) (2.00 x 106) X (8.71 x 100)
6.) (2.95 x 106) X (8.41 x 10-2)
7.) (8.23 x 10-2) X (4.43 x 10-4)
8.) (-5.03 x 107) X (6.3 x 103)
9.) (2.41 x 108) X (-6.29 x 103)
10.) (7.63 x 106) X (9.11 x 10-4)
11.) (5.30 x 103) X (7.3 x 107)
12.) (-6.0 x 102) X (-2.46 x 102)
13.) (6.89 x 107) X (-6.43 x 10-1)
14.) (5.47 x 102) X (5.74 x 10-3)
15.) (-6.24 x 10-7) X (7.85 x 10-1)
16.) (4.47 x 103) X (3.6 x 10-4)
17.) (1.68 x 105) X (5.3 x 102)
18.) (1.68 x 105) X (5.2 x 102)
Dividing Numbers in Scientific Notation:
When you divide numbers in scientific notation you first divide the coefficients then subtract the powers. After that you
make sure you have the coefficient written in proper format. If you move the decimal  you increase the power by
how many spaces you moved the decimal. If you move  the decimal you decrease the power by how many spaces you
moved the decimal.
14
-23
(2.35x10 ) ÷ (3.25x10 )
Divide the following numbers:
1.) (1.2 x 103) ÷ (5.7 x 104)
2.) (3.78 x 100) ÷ (6.79 x 103)
3.) (8.74 x 104) ÷ (9.1 x 105)
4.) (4.21 x 103) ÷ (5.0 x 104)
5.) (2.00 x 106) ÷ (8.71 x 100)
6.) (2.95 x 106) ÷ (8.41 x 10-2)
7.) (8.23 x 10-2) ÷ (4.43 x 10-4)
8.) (-5.03 x 107) ÷ (6.3 x 103)
9.) (2.41 x 108) ÷ (-6.29 x 103)
10.) (7.63 x 106) ÷ (9.11 x 10-4)
11.) (5.30 x 103) ÷ (7.3 x 107)
12.) (-6.0 x 102) ÷ (-2.46 x 102)
13.) (6.89 x 107) ÷ (-6.43 x 10-1)
14.) (5.47 x 102) ÷ (5.74 x 10-3)
15.) (-6.24 x 10-7) ÷ (7.85 x 10-1)
16.) (4.47 x 103) ÷ (3.6 x 10-4)
17.) (1.68 x 105) ÷ (5.3 x 102)
18.) (1.68 x 105) ÷ (5.2 x 102)