Chem One Online Support Course

Module # 1
Topics and Concepts
Page 6


Solutions to Problems
Reports
Laboratory
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Scientific Notation:

Scientific Notation is a convenient way of expressing very large numbers or very small numbers in written form without using a whole lot of zeros.

The mechanics of converting numbers into scientific notation and vice versa are presented here.
( If you want to know more about the mathematics behind the derivation of scientific notation please go to Other Links and Sites (side bar). Several Web Site links are listed under the category Scientific Notation.)

To convert regular numbers into scientific notation:

1. Find the decimal point in the number.
   600000     The decimal point is after the last zero
 .0000006   The decimal point is before the first zero
 623000.5   The decimal point is in between two digits
2. The object is to move the decimal point in a direction (left or right) so that only one digit to the left of the decimal point remains.
   600000     becomes 6.00000
 .0000006   becomes 0000006.
 62350000.   Becomes 6.2350000
3.

In order to show how many places (or place values) you have moved the decimal you must multiply the final answer by 10 raised to an exponent.
The exponent of the ten (10) must be equal to the number of places you moved the decimal.
 One other important point: The exponent will be + or - depending on which way (left or right) that you have moved the decimal.
Sounds complicated? Not really. See what happens to the numbers from step 2.
 

6.00000 becomes 6 X 105
 0000006. becomes 6 X 10 - 7
 6.2350000 becomes 6 .235 X 107

Notice how the zeros were dropped. The exponent in each case is the number of digits the decimal point was moved to the left (positive direction) or the right (negative direction).

Sometime students confuse the number line in algebra with the directions of the movement of the decimal in scientific notation. Scientific Notation is not a movement along a number line therefore the directions of positive and negative that apply to the algebra number line do not apply here.

 

Conversion of Scientific Notation numbers back into regular numbers essentially follows a reverse process of the above table.

1. Find the decimal point in the number.
   7 X 105   The decimal point is after the seven
 6.5 X 10 - 6   The decimal point is between two digits
2. The objective is to move the decimal point the same number of digits equal to the value of the exponent of the ten (10). The sign of the exponent tells you which direction (left or right) the decimal was originally moved from.
 

7 X 105   positive 5 means the decimal point was originally moved from the right -- thus the original number is 700000.

 6.5 X 10 - 6   the negative - 6 means the decimal point was originally moved from the left -- thus the original number is .0000065

Notice, that this time, the zeros were added in order to show how many digits (or place values) the decimal point was moved.

 

You will find Examples of how to convert between regular numbers and Scientific Notation in the Example Problems Pages of this Web Site.
You may use the side bar link, as well:    Go to the Example Page. All Links to Scientific Notation Examples are listed in a Table.

Page 7 addresses the topic of addition, subtraction, multiplication, and division of Scientific Notation numbers.

Forward to Page 7