The Basics: Powers of Ten and Scientific Notation

 

       The Basics: 
Scientific Notation and Powers of Ten

Scientific notation is commonly used in mathematics to represent positive or negative numbers that are extremely large or close to zero.   Numbers are written as a decimal number between one and 10 (including 1, but excluding 10) multiplied by some integral power of 10. 

To write a number that is in standard form in scientific notation, move the decimal point in the given number to a position so that the number is between 1 and 10 (excluding 10.) Then determine how many places and in what direction the decimal point was moved.

• A decimal movement n places to the left means that we write the decimal number (between 1 and 10) multiplied by 10 to the power of n.

                    Example:  $215=2.15\:\times10^2$  

• A decimal movement n places to the right means that we write the decimal number (between 1 and 10) multiplied by 10 to the power of $-n$. 

                    Example:  $.00215=2.15\:\times10^{-3}$

• Reverse these steps if you need to convert a number in scientific notation to a number in standard form.  If the exponent is positive, move the decimal point to the right.  If the exponent is negative, move the decimal to the left.

                    Example:  $2.15\times10^2=215\:\:\:or\:\:\:\:\:2.15\:\times10^{-3}=.00215$

Watch these helpful Khan Academy videos for more information:

1. Scientific Notation (old) Links to an external site.
2. Scientific Notation Examples Links to an external site.

Now move on to the energy technology video demonstrations. When you are ready, take the practice quiz to show what you know. If you think you need more practice, ask your instructor if the optional practice assignments would help you.