scientific notation : means of expressing very large or very small numbers in a compact form, to simplify computation. In this notation any number is expressed as a number between 1 and 10 multiplied by the appropriate power of 10.

For example, 32,000,000 in scientific notation is 3.2 107, and 0.00526 is 5.26 10-3.


Converting from standard to scientific notation

To convert a number to scientific notation, the decimal point must first be located. In 35,467, for example, the decimal point is at the end of the number. Next, one must determine where the decimal point would need to be located for the number to be greater than or equal to 1 and less than 10. In the given number, the decimal should be moved between the 3 and the 5. This gives the new number 3.5467.

An interesting fact to note is that multiplying a decimal number by a power of ten is equivalent to moving the decimal point a certain number of spaces to the right (where that number is equal to the power of ten in the multiplier). Therefore, multiplying by a negative power of ten moves the decimal place a certain number of places to the left. This concept is key in understanding scientific notation.

Now, one must find out how many places the decimal point was moved, and in which direction it would need to be moved in order to restore the original number. In creating 3.5467, for example, the decimal was moved 4 places. Also, one would need to move it to the right to change it back to 35,467.

Finally, this information is to be applied towards the creation of a term in scientific notation. First, the number between 1 and 10 must be written down. Next, because it is being multiplied by some power of ten to be equal to the original number, "x 10" is added to the term. Lastly, the exponent is tacked on to the 10. Use the direction previously found (where left corresponds to negative and right is positive) and the number of places found to determine the value of the exponent. In our example, this gives us 3.5467 x 103.

One common form of shorthand used by calculators and computers substitutes the letter "E" for the expression "x 10n". For example, while one might write out 1763 as 1.763 x 103, it would be expressed on a calculator as 1.763E3. This is also how scientific notation is expressed on the Units Convertor on this site.


91,022,103 = 9.1022103 x 107

0.0013 = 1.3 x 10-3

Converting from scientific to standard notation

The reverse conversion process is much easier. To convert a number from scientific notation (such as 3.08 x 105) to decimal notation, one must only multiply the two terms together. In this case, the result is 308,000.