UNIT # 1 Introduction Objectives Reading 1.1 Metric System 1.2 1.3 Scientific Notation 1.4 Dimensional Analysis 1.5 1.6 1.7 1.8 Problems 1 | 2 | 3

MEASUREMENT

1.3 - Scientific Notation

Scientific notation is a very useful system of writing figures that are extremely large or extremely small. Scientific notation uses exponents to express figures.

For example,

• 1,000,000 can be written as 1 x 106.
• This is ten raised to the power of six
Similarly,
• 0.000001 can be written as 1 x 10-6
• This is ten raised to the power of negative six
Suppose we have a measurement of 6765.44 g and we wish to express this measurement in scientific notation. We simply move the decimal over to the LEFT until there is one digit (from 1 to 9) to the left of the decimal point. Here, we move the decimal place three places to the left. Therefore, in scientific notation,

6765.44 g = 6.76544 x 103 g.

Suppose we have a measurement of 0.000004334 cm and we wish to express this measurement in scientific notation. We simply move the decimal over to the RIGHT until there is one digit (from 1 to 9) to the left of the decimal point. Here, we move the decimal place six places to the right. Therefore, in scientific notation,

0.000004334 cm = 4.334 x 10-6 cm.

Do you understand the powers of ten?

View this site as it takes you from:

 1023 meters (10 millions light years away from the Milky Way) 10-16 meters (examining quarks)

Later on you in section 1.6 you will appreciate the use of scientific notation in expressing a measurement in its proper number of significant figures.

Section 2.7
Exponents, Exponential Notation & Scientific Notation ..p27

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