What is Scientific notation?

Scientists and engineers often have to deal with super huge (like 6,000,000,000,000,000,000,000) and super small numbers (like 0.0000000000532) . How can they do this without tiring their hands out? How can they look at a number and understand how large or small it is without counting the digits? The answer is to use scientific notation. If you come to this tutorial with a basic understanding of positive and negative exponents, it should leave you with a new appreciation for representing really huge and really small numbers!

To express large number in short way, scientists have developed a method and this is called Scientific Notation. It is also known as Standard Form. It is generally expressed as

a × 10ⁿ

Here, 'a' is coefficient and a real number whereas n is a integer. The value of  'a' will be 1 ≤ a < 10. So 'a' going to be greater than or equal to 1, and it  will be less than 10.

So, let's see how can we represent large number in scientific notation whether it  is positive or negative.

Suppose the number is 0.0002077. It's scientific notation will be 2.077 x 10^-4. More examples are below.

 245,600,000,000  ---    2.456 × 10¹¹

 13,040,000           ---    1.304 × 10⁷

− 53,000                ---    − 5.3 × 10⁴ 

0.0000000003457      ---    3.457 ×  10^-10  

As you can see, the exponent of 10 is the number of places the decimal point must be shifted to give the number in long form. A positive exponent shows that the decimal point is shifted that number of places to the right. A negative exponent shows that the decimal point is shifted that number of places to the left. 

Most calculators and many computer programs present very large and very small results in scientific notation, typically invoked by a key labelled E.