# What is scientific notation used for?

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^b.

For example, we write 350 as 3.5 × 10^2 or 35 × 10^1 or 350 × 10^0.

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

Thus, we write 350 as 3.5 × 10^2.

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 × 10^23 than $\text{602 200 000 000 000 000 000 000}$.

For tiny numbers such as the mass of a hydrogen atom, it is easier to write 1.674 × 10^"-24"color(white)(l) "g" than
$\text{0.000 000 000 000 000 000 000 001 674 g}$

.

Another reason to use scientific notation is this:

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

Writing the number as 6.022 × 10^23 shows that the precision is only to four significant figures.