Scientific Notation

It is often difficult to read and work with very large or very small numbers.

For example,

• In mid-2002, the U. S. national debt was approximately $5,600,000,000,000. To calculate the amount of money owed by each American, we would divide this number by the U. S. population. Unfortunately, 5600000000000 will not fit in the display of most calculators.

• The rest mass of an electron is about 0.000000000000000000000000000000911 kilograms. It is very difficult to work with a number that has so many zeros.

Numbers such as 0.000000000000000000000000000000911 and 5,600,000,000,000 are said to be written in expanded form.

To make it easier to read and work with very large or very small numbers, we often use scientific notation.

For example, 2.1 × 10⁵ is written in scientific notation.

In expanded form we write, 2.1 × 10⁵ = 2.1 · 10 · 10 · 10 · 10 · 10 = 210,000.

 

Definition — Scientific Notation

A number is written in scientific notation when it has the form N × 10ⁿ where 1 ≤ N < 10, N is written in decimal notation, and n is an integer.