Purpose
The purpose of this exercise is to learn about scientific notation and how to perform
mathematical operations with numbers written in scientific notation.
Introduction
Scientific notation is a useful way of writing very large and very small numbers. It is
easier to carry out calculations with such numbers when they are written in scientific notation.
When measured quantities are expressed in scientific notation, the number of significant figures
is clearly shown. Scientific notation is a system in which an ordinary decimal number is
expressed as a product of a number between 1 and 10 multiplied by 10 raised to a power. The
number between 1 and 10 is called a coefficient and is written first. The number 10 raised to a
power (exponent) is called an exponential term. The coefficient is always multiplied by the
exponential term. The scientific notation form of the number 6022 is
Coefficient Exponent
6.022 x 103
Multiplication sign Exponential term
A brief review of exponents and their use is helpful before we consider the rules for
converting ordinary decimal notation to scientific notation. An exponent is a number written as a
superscript following another number and indicates how many times the first number, the base, is
to be multiplied by itself. For example:
72 = 7 x 7 = 49
25 = 2 x 2 x 2 x 2 x 2 = 32
103 = 10 x 10 x 10 = 1000
Because scientific notation utilizes exponential terms with base 10, let’s look more closely at
these terms.
For exponents larger than 1 :
Decimal Form Exponential form
1 100
10 101
100 = (10) (10) = 102
1000 = (10) (10) (10) = 103
10,000 = (10)(10)(10)(10) = 104
Notice that the exponent indicates how many times the number 1 is multiplied by 10 and how
many places the decimal point is moved to the right..
For example, 101 = 10; 102 = 10 x 10; 103 = 10 x 10 x 10 = 1000; and so forth.
SCIENTIFIC NOTATION
Worksheet
Name: _______________________ Score: ______
Lab Day/Time: ___________ Date: _________
Write the following numbers in exponential form:
10 000 000 = _______________ 1 million _______________
100 000 000 000 000 000 = _______________
Write the following exponential terms in ordinary decimal form:
109 = _____________________ 106 = ___________________
For exponents smaller than 1 :
Decimal Form Exponential form
0.1 10-1
0.01 10-2
0.001 10-3
Notice that a negative exponent indicates how many times the number 1 is divided by 10, and
how many places the decimal point is moved to the left. Negative exponents indicate reciprocals:
10-1 = 1 = 0.1 10-2 = 1 = 0.01 10-3 = 1 = 0.001
101 102 103
Write the following numbers in exponential form:
0.00001 = _________________ 0.000000000000000000001 = ___________
Write the following exponential terms in ordinary decimal form:
10-7 = ___________________________ 10-6 = _________________________
In scientific notation, 1,201 = 1.201 x 1000 = 1.201 x 103.
Similarly, 0.001201 = 1.201 = 1.201 = 1.201 x 10-3
1000 103