Scientific Notation

 

Scientific notation was developed to make it easier dealing with large numbers, 40,000,000,000 and small numbers 0.000000000000053.

 

The basic form is,

 

N x 10n,

 

where N is a number between 1.0 and 9.9 and it is multiplied by 10 raised to the nth power.  An@ is a positive or negative integer or zero.

 

When you see a number like 109, it really means 1 x 109.

 

Some examples: 103 = 1000, 102 = 100, 10-3 = 0.001, 10-6 = 0.000001

 

To change from scientific notation to regular notation when n is positive all you need to do is move the decimal point to the right An@ times.  Zeros are added to fill the places created by the moving decimal place.  For example,

 

3.4 x 106 = 3,400,000.0 (the decimal moved to the right 6 places)

 

To change from scientific notation to regular notation when n is negative all you need to do is move the decimal point to the left An@ times.  Again zeros are added in to fill the places created by moving the decimal.  For example,

 

5.87 x 10-8 = 0.0000000587 (the decimal moved to the left 8 places)

 

To multiply two numbers in scientific notation, you multiply the numbers in front of the powers of ten and add the powers of ten.  If you want to, you can than adjust the decimal and the powers of ten to make the number AN@ greater than 1 and less than 10.

 

Example:   (3.0 x 107) x (4.0 x 10-10) = 12.0 x 107-10 = 12.0 x 10-3 = 1.2 x 10-2

 

To divide two numbers in scientific notation, you divide the numbers in front of the powers of ten and subtract the denominator=s power of ten from the numerator=s.  If you want to, you can then adjust the decimal and the powers of ten to make the number AN@ greater than 1 and less than 10.

 

Example:   (3.0 x 107) x (4.0 x 10-10) = 0.75 x 107-(-10) = 0.75 x 1017 = 7.5 x 1016

 

Note that 100 = 1 (This is necessary if dividing a number by itself is going to give the correct answer, namely 1!)