If you've ever been confused by a calculated result that includes an "E" in the number, this page will eliminate that confusion once and for all.
This free online conversion calculator will convert a scientific notation into a decimal number, or vice versa.
Plus, the converter will accept notations in three different formats: 3.5E4, 3.5e4, or 3.5 x 10^4.
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.
In fact, 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 a number of interested parties:
Scientific notation allows you to abbreviate the above number to the following (note that the "E" or "e" simply stands for "power of 10 exponent"):
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:
Again, SN eliminates the chance of the exact number getting lost in translation.
Without getting into the underlying math used to convert Decimals to SN, the conversion process is simply 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 moved the decimal point to the right, the power of 10 exponent is negative.
So in the example above, to convert 123000000000000 to a scientific notation you simply 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.
Or, to convert 0.0000000000123 to a scientific notation you simply 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.
To convert SN to a decimal number, you simply 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 simply 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.
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.
Finally, you might find it interesting to know that in building this converter I actually 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 let me know the number you entered if it appears the converted result is "NaN" (Not a Number) or otherwise appears incorrect.
With that, let's use the Scientific Notation Converter to convert to and from a decimal number (also referred to as regular notation).
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To Help You To
Enter number: Enter either a decimal number (regular notation) to convert to scientific notation (also sometimes referred to as exponential or standard notation), or a scientific notation to convert to a decimal number. Note that you can enter scientific notation in any of these formats: 35e7, 35E7, or 35 x 10^7 (the up arrow "^" can be entered by pressing the number 6 key while holding down the Shift key on most keyboards).
Converted number: This result is either an exponential notation or a decimal number (regular notation), depending on which type of number you entered at the top of the converter.
Positive exponents: If the scientific notation contains a positive exponent (1.12 x 105), this translates to 1.12 x 100000. And since 1.12 x 100000 = 112000, the scientific notation 1.12 x 105 is equal to 112000 (or, you can achieve the same result simply by moving the decimal point 5 places to the right).
Negative exponents: If the scientific notation contains a negative exponent (1.12 x 10-5), this translates to 1.12 x 1/100000 (a negative exponent indicates 1 over the base raised to the power of the exponent), which then becomes 1.12/100000. And since 1.12 ÷ 100000 = 0.0000112, the scientific notation 1.12 x 10-5 is equal to 0.0000112 (or, you can achieve the same result simply by moving the decimal point 5 places to the left).