What is Scientific Notation?
Scientific notation (SN), also referred to as exponential notation, is a system developed to abbreviate numbers having an extreme number of digits and or decimal places.
You can think of SN as a short-hand method for expressing numbers.
To illustrate the usefulness of abbreviating numbers, suppose you need to communicate the following number to one or more interested parties:
Scientific notation allows you to abbreviate the above number to the following (note that the "E" or "e" stands for "power-of-10 exponent"):
Which might also be expressed as:
1.23E14
or
1.23e14
Can you see how the chances of the miscounting the number of zeros while the number is being passed around is eliminated with the use of SN?
Or, if you are communicating a very small number, like the following:
Then, scientific notation allows you to abbreviate the above decimal number to the following:
Which might also be expressed as:
1.23E-11
or
1.23e-11
Again, SN eliminates the chance of the exact number getting lost in translation.
How to Convert a Decimal Number to Scientific Notation
Without getting into the underlying math used to convert Decimals to SN, the conversion process is to move the decimal point left or right until the number becomes a number between 1 and 10.
The number of places you must move the decimal point to cause the number to fall between 1 and 10 becomes the power-of-10 exponent.
If you need to move the decimal point to the left, the power-of-10 exponent is positive. Otherwise, if you need to move the decimal point to the right, the power-of-10 exponent is negative.
So in the example above, to convert 123000000000000 to scientific notation, you move the decimal point to the left until the number to the left of the decimal point (coefficient) is a number from 1 to 9, which in this case is 14 places.
123000000000000
Converts to the scientific notation:
1.23 x 1014
| 1. | 2 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
Or, to convert 0.0000000000123 to scientific notation, you move the decimal point to the right until the number to the left of the decimal point (coefficient) is a number from 1 to 9, which in this case, is 11 places.
0.0000000000123
Converts to the scientific notation:
1.23 x 10-11
| 0. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1. | 2 | 3 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
How to Convert Scientific Notation to a Decimal Number
To convert SN to a decimal number, you start with the number left of the multiplication sign (or "E") and move the decimal point right (if positive exponent) or left (if negative exponent) the number of places indicated by the power-of-ten exponent.
As you move the decimal point, add zeros for placeholders as needed.
So to convert the scientific notation 1.23 x 1014 to regular notation you simply move the decimal point 14 places to the right, as indicated by the exponent 14.
1.23 x 1014
Converts to the decimal number:
123000000000000
| 1 | 2 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
Or, to convert the scientific notation 1.23 x 10-11 to regular notation you simply move the decimal point 11 places to the left, as indicated by the exponent -11.
1.23 x 10-11
Converts to the decimal number:
0.0000000000123
| . | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 3 |
| 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
Scientific Notation Conversion Chart
The following are some popular standard form numbers converted to scientific notation.
| Text | Number | SN |
|---|---|---|
| one thousand | 1,000 | 1 x 10^3 |
| ten thousand | 10,000 | 1 x 10^4 |
| hundred thousand | 100,000 | 1 x 10^5 |
| one million | 1,000,000 | 1 x 10^6 |
| ten million | 10,000,000 | 1 x 10^7 |
| hundred million | 100,000,000 | 1 x 10^8 |
| one billion | 1,000,000,000 | 1 x 10^9 |
| ten billion | 10,000,000,000 | 1 x 10^10 |
| hundred billion | 100,000,000,000 | 1 x 10^11 |
| one trillion | 1,000,000,000,000 | 1 x 10^12 |
A Related Note About the Converter
You might find it interesting to know that in building this converter, I had to write the code so that the entered notations are converted to text strings because the scripting language I use to create calculators automatically returns large and small numbers in ... you guessed it ... scientific notation!
Of course, since I can't test the manipulation of text strings for all possible numbers, be sure to use the feedback form beneath the calculator to let me know the number you entered if it appears the converted result is "NaN" (Not a Number) or otherwise appears incorrect.