Introduction To Scientific notation

In our real life we come across many situations and numbers which are very large. Like let us take an example , the speed of light in vacuum is  299792.5 km per second. It is approximated as 300000 km per second or as 300,000,000 meter per sec and similarly if we take one more example of  mass of the earth is 5,976,000,000,000,000,000,000,000 kg. These type of numbers are very difficult to read and write. For making them more convenient we write these number by using exponents with base 10 .like speed of light in vaccum we can write as  3 x 10⁸ meter per second. such a  form of a number is known as the standard form.

Scientific Notation

Definition of Standard form 
Mathematically definition of standard form : A number is said to be in standard form  , if it is expressed as the product of a number between 1 and 10 ( including 1 but excluding 10) and a positive integer power of 10.

The standard notation is nothing but the regular form of number whereas the standard form of a number is known as scientific notations

How to do scientific notation
We use the following method to write large number in the scientific notation
• Obtain the number and move the decimal to the left  till we get just one digit left to the decimal point
• Write the given number as the product of the number  so obtained and 10ⁿ , where n is the number of places the decimal point has been moved to the left.
• If the number is between 1 and 10 , then write it as  the product of the number itself and 10⁰.
Let us take some example to see how to do scientific notation

Examples based on scientific notation
Example: For given number , convert to scientific notation
(i) 393568
       To convert it into scientific notation we will use following steps:
     •   Here  we will move the decimal point to five places to obtain a number  where there is just one digit to the left of decimal point
           Therefore  393568= 3.93568  x 10 ⁵
(ii) In  this example  we will learn procedure of adding scientific notation
            3 × 103         and            4.2 × 10⁴
          For addition of the given scientific notation ,
=>  3 x 10³  + 4.2 x 10⁴
=> Step1: we will change it to same indicies
=> 0.3 x 10⁴ + 4.2 x 10⁴
=> (0.3 + 4.2)x 10⁴
=> 4.5 x 10⁴ ans