What is scientific notation used for?

1 Answer
Mar 21, 2014

Answer:

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"#

.

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.