What is scientific notation used for?

1 Answer
Mar 21, 2014

Scientific notation is used to write numbers that are too big or too small to be conveniently written in decimal form.

Explanation:

In scientific notation, we write a number in the form a×10b.

For example, we write 350 as 3.5×102 or 35×101 or 350×100.

In normalized or standard scientific notation, we write only one digit before the decimal point in a.

Thus, we write 350 as 3.5×102.

This form allows easy comparison of numbers, as the exponent b gives the number's order of magnitude.

For huge numbers such as Avogadro’s number, it is much easier to write 6.022×1023 than 602 200 000 000 000 000 000 000.

For tiny numbers such as the mass of a hydrogen atom, it is easier to write 1.674×10-24lg than
0.000 000 000 000 000 000 000 001 674 g

.

Another reason to use scientific notation is this:

Most of the zeroes in a number such as 602 200 000 000 000 000 000 000 are completely meaningless. They serve only to locate the decimal place.

Writing the number as 6.022×1023 shows that the precision is only to four significant figures.