Question

What is scientific notation used for?

Answer 1

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 `"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
`"0.000 000 000 000 000 000 000 001 674 g"`

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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 × 10^23` shows that the precision is only to four significant figures.