DEFINTIONS AND WORKSHEET
SCIENTIFIC NOTATION
Large and small quantities are normally expressed using a format, termed
“scientific notation” (= SN). A straightforward reason exists to use scientific
notation: it is extremely cumbersome to write out large or small numbers with all
the necessary 0’s.
Numbers expressed in scientific notation are formatted like this: ##.# x 10E ,
where # represents a number, “x” is the symbol for “times” and “E” is the
exponent or power of 10. The exponent gives the number of times 10 is
multiplied by itself in order to represent a number.
Examples: 103 = 10 x 10 x 10 = one thousand = 1000 = 1 x 10 3
236 = 2.36 x 102
= 2.36 x 10 x 10 = two hundred, thirty-six
The number 1 is expressed as 100.
Numbers between 0 and 1 (very small numbers) are expressed as negative
powers of 10.
Example: 10-3 = 0.001 = (1  1000) = 1  (10 x 10 x 10).
Multiplication and division of large (small) numbers is made easier using this
notation, once you become familiar with the rules:
To multiply two or more numbers expressed in SN, multiply the leading numbers
and ADD the exponents. To divide two or more numbers expressed in SN,
divide the leading numbers and SUBTRACT the exponents.
Examples: 1,000
X 10,000 = 10,000,000 or
1.0  103 X 1.0  104 = 1.0  107
100,000  100
= 1,000
or
5
2
3
1.0  10  1.0  10 = 1.0  10
SCIENTIFIC NOTATION WORKSHEET
Work the following examples, to insure that you understand how to manipulate
numbers in scientific notation.
(1) Try these by hand:
1012 X 104 =
10-3 X 107 =
1014 X 108 =
10-17 X 109 =
103
 105 =
1023  10-3 =
1010  107 =
10-3  108 =
(2) Try these using a calculator:
(3.1 x 1010) X (4.6 x 104 )  (9.4 x 10-3) =
(7.23 x 10-1) X (2.9 x 105) =
1012 X (5.0 x108) X (3.33 x 100) =
(4.6 x 10-23) X 106 =
(5.0 x 103)  (2.5 x 105) =
(1.12 x 103)  10-3 =
(7.8 x 1010)  107 X (3.14 x 10-7) =
(3.9 x 10-3) X 108  (6.77 x 105) =
(3) Express these numbers in the standard format
101
=
10-3 =
1010 =
10-4 =
103
=
100 =
107 =
10-5 =
(4) Express these numbers in scientific notation
4.56
=
10,000
=
0.0355
=
12,010,000 =
0.000322
=
0.15
=
4 billion
=
256,000
=