What is the purpose and advantage of using scientific notation?
Scientific notation is used where the number to be represented is too large to be written as a complete number. Or when the answer we get requires a lower level of precision. Also, using the scientific notation makes operations between large numbers easier with a reduced possibility of error.
For example if you are using the speed of light in any formula its exact value is 299,792,458 m/s but we usually write it as 3*10^8 m/s. Similarly a distance of 23456776 m can be written as 2.34*10^7 m.
While using the scientific notation what has to be kept in mind is the number of relevant significant places. When the speed of light used is 299,792,458, we get an answer which is accurate to the meter. When we denote it by 3*10^8, the level of accuracy decreases. So, if you are calculating the distance travelled by light in 10 years, and require an answer accurate to the kilometer you would use 2.99792*10^8. If you want the answer to be less accurate as light travels such a large distance in 10 years that even an answer in terms of billions of kilometers would suffice, just using 3*10^8 is enough.