We often have to write out very large numbers or very small numbers. For example, the United States population is about 372,300,000, and the population of the world is about 7,800,000,000.
That’s a whole lot of zeros. You are probably familiar with the words thousand, million, billion. We would usually shorten the population numbers by saying:
- US population is 372.3 million.
- Global population is 7.8 billion.
In computers/phones, you have probably hears the prefixes kilo-, mega-, giga-, and tera-. (for example, an app may be 13 megabytes, and a video may be 2.3 gigabytes.
Scientific notation
In science, instead of using these words we often express a number by just writing the number with a “x10#“. Here is a table of different ways to express really big or really small numbers:
| Number | Name | Prefix | x10# | example |
|---|---|---|---|---|
| 1,000 | thousand | kilo- | 3 | kilometer |
| 1,000,000 | million | mega- | 6 | a phone app might be in megabytes |
| 1,000,000,000 | billion | giga- | 9 | a movie would be measured in gigabytes |
| 1,000,000,000,000 | trillion | tera- | 12 | larger computer hard drives now can store terabytes of data. |
| 0.001 | thousandth | milli- | -3 | Vitamin doses are usually measured in milligrams. |
| 0.000,001 | millionth | micro- | -6 | cells sizes are often measured in micrometers |
| 0.000,000,001 | billionth | nano- | -9 | nanotechnology refers to technology where devices are so small they are measured in nanometers |
| 0.01 | hundredth | centi | -2 | $0.59 = 59 cents |
Standard scientific notation
In math and science, these ‘scientific notation’ or ‘exponential notation’ are always written with only one digit before the decimal dot, then any numbers after the decimal, and finally the ‘x10#.’
Examples
| Number | Scientific notation |
|---|---|
| 6.25 million | 6.25 x 106 |
| 1,258 | 1.258 x 103 |
| 0.0042 | 4.2 x 10-3 |
| 3,200,000,0000,000 | 3.2 x 1012 |
Solving math problems
When multiplying or dividing, simply use the two numbers before the ‘x’ and handle them as if the x 10# wasn’t there. For the exponents on the 10’s, just add them when multiplying, and subtract them when dividing.
Videos
How to set up numbers expressed as scientific notation:
How to multiply or divide numbers written in scientific notation.