CK-12 Physical Science Concepts - For Middle School

http://www.ck12.org Chapter 1. Introduction to Physical Science

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Using Scientific Notation

It’s easier to convert numbers to and from scientific notation than you might think. Refer to the examples on the
chalkboard in theFigure1.31 as you read the following steps. Follow the steps in the sequence listed here to convert
a number to scientific notation. Follow the steps in the reverse order to convert a number from scientific notation.

1. Move the decimal point left or right until you reach the last nonzero digit. This new decimal number isaina
   × 10 b.


2. Count how many places you moved the decimal point in Step 1. This number isbina× 10 b.


3. Did you move the decimal point left (first example in theFigure1.31)? If so,bis positive. Did you move the
   decimal point right (second example in theFigure1.31)? If so,bis negative.

FIGURE 1.31

These two examples show how to convert

large and small numbers to scientific no-

tation.

Q:Apply the steps above to write 450,000 in scientific notation.

A:The unwritten decimal point in this number follows the last zero. Move the decimal point from this position to
the left and stop just before the last digit, giving you 4.5 fora. The decimal point was moved five places to the left,
sob is 5. In scientific notation the number is 4.5× 105.

Q:Apply the steps in reverse order to write the number that is expressed as 7.2× 104 in scientific notation.

A:Add zeroes to 7.2 as you move the decimal point four places to the right. This gives you the number 72,000.

Summary

• Scientific notation is a way of writing very large or very small numbers that uses exponents. Numbers are
  written in the formata× 10 b.


• Changing numbers to or from scientific notation is easy to do by following three simple steps.