Exponents and Variables: Scientific Notation

Scientific notation is used to write very big or very small numbers in decimal form.
-  In scientific notation, all numbers are written in the form of: , where is greater than 1 and less than 10.

-  To convert a number from scientific notation to standard form, move the decimal point to the left (if the exponent of ten is a negative number), or to the right (if the exponent is positive).

Examples:

Example 1.  Write in scientific notation.
Solution: First, move the decimal point to the right so you have a number between and . That number is . Now, determine how many places the decimal moved in step by the power of . We moved the decimal point 4 digits to the right. Then: → When the decimal moved to the right, the exponent is negative. Then:

Example 2.  Write in standard notation.
Solution: The exponent is negative 5. Then, move the decimal point to the left five digits. (remember ) When the decimal moved to the right, the exponent is negative. Then:

Example 3.  Write in scientific notation.
Solution: First, move the decimal point to the right so you have a number between 1 and 10.  Then: , Now, determine how many places the decimal moved in step 1 by the power of 10. → Then:

Example 4.  Write in standard notation.
Solution: → The exponent is positive 5. Then, move the decimal point to the right five digits. (remember ) Then: