This calculator converts numbers to and from scientific notation, also known as standard form, in both directions. Scientific notation writes any number as a coefficient between 1 and 10 multiplied by a power of ten, which is how scientists, engineers and statisticians handle the very large and very small numbers that would otherwise be a clutter of zeros. The mass of the Earth, the size of an atom and the national debt are all far easier to read and compare once written this way. The first tool takes an ordinary number and returns its scientific notation, showing the coefficient, the exponent and the order of magnitude, which is just the power of ten that tells you the rough size of the value. The second tool runs the other way, taking a coefficient and an exponent and expanding them back into the full decimal number. Converting by hand means shifting the decimal point until one non-zero digit sits in front of it and counting the places you moved, with the count becoming the exponent, positive for large numbers and negative for small decimals. The calculator does that counting for you and keeps the result exact within normal precision. Enter a value in either box to see the conversion update as you type.
To convert a number to scientific notation, the calculator finds the power of ten so that dividing by it leaves a coefficient between 1 and 10, then rounds the coefficient to your chosen significant figures. To convert back, it multiplies the coefficient by ten raised to the exponent, expanding the value to a normal decimal.
The number 4500 becomes 4.5 times 10 to the power 3, since the decimal moves three places left. The notation 2.3 times 10 to the power minus 3 expands to 0.0023, since the decimal moves three places right.
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