What are practical uses of scientific notation?

Answer 1

By using scientific notation very large and very small numbers can be more easily written, and allows for less chance of error. Scientific notation is particularly used by Astronomers, chemists and physicists.

For example the nearest star to us is approximately 25000000000000 miles or 40000000000000 km away from us. Written like that not only are the numbers cumbersome but there is a risk of error in missing out one or more of the zeros. Using scientific notation, the distances become much easier to handle: 2.5 × 10^13 miles or 4 × 10^13 km.

Similarly, a mole of an element contains approximately 602210000000000000000000 atoms. Again, this is much easier to write, read and use in scientific notation: 6.0221 × 10^23

A proton weighs approx 0.0000000000000000000000000016726 kg, or 1.6726 × 10^-27 kg in scientific notation.

However, an abbreviated form of scientific notation* is used in everyday life, particularly on the news. The national debt of USA at the beginning of the year was approx $18.96 trillion. But what does this mean? 1 trillion = (10^3)^(4+1) = 10^15, so the national debt was approx $18.96 × 10^15 which is almost scientific notation (to be scientific notation it would be $1.896 × 10^16); similarly talking about the population of an area of 6.5 million people: 1 million is 10^6, so this is 6.5 × 10^6 (scientific notation).

* Actually what is being used is engineering notation which is a form of scientific notation in which the power of the 10 is a multiple of 3, and the number before the "× 10^" does not have to be greater than or equal to 1 and less than 10.

Answer 2

The most common use for scientific notation is that the numbers (which are very large) can be expressed in a small area and are easier to work with.