Adding Scientific Notation

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Scientific notation is the way to write any large number into shortest form, it is written as the product of a number between 1 and 10 and a number that is a coefficient of 10, which means the base should be 10.It is very useful to calculate or to write also. For example, we know that the speed of light is 3x10^8 m/s but if do not use the scientific notation it will be written as 300000000 m/s which is the conventional form. 

Now, we have to see how we can add two numbers given in scientific notation:

2.38 x 10^3 + 4.62 x 10^2

Step 1: First check which has a smaller coefficient and which has larger.

Step 2: make the larger coefficient into equal to the smaller coefficient or vice versa.

Step 3: to make equal we can divide or multiply by 10.

Step 4: If the coefficient is equal we can directly add other numbers and write the final term with the same coefficient with base 10.

 2.38 x 10 x 10^2 + 4.62 x 10^2

 Or,    23.8 x 10^2 + 4.62 x 10^2

 Or,    28.42 x 10^2.


Example: 1.345×10^5 + 5.0023×10^8

Solution: 1.345 x 10^5 + 5.0023 x 1000 x 10^5

1.345 x 10^5 + 5002.3 x 10^5

 5003.645 x 10^5


Example: 2.5 x 10^-5 + 4.5 x 10^-6

Solution: 25 x 10^-1 x 10^-5 + 4.5 x 10^-6

 25 x 10^-6 + 4.5 x 10^-6

 29.5 x 10^-6





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