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 × 10^ba×10b.

For example, we write 350 as 3.5 × 10^23.5×102 or 35 × 10^135×101 or 350 × 10^0350×100.

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

Thus, we write 350 as 3.5 × 10^23.5×102.

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

For huge numbers such as Avogadro’s number, it is much easier to write 6.022 × 10^236.022×1023 than "602 200 000 000 000 000 000 000"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^"-24"color(white)(l) "g"1.674×10-24lg than
"0.000 000 000 000 000 000 000 001 674 g"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"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 × 10^236.022×1023 shows that the precision is only to four significant figures.