Convert a number to scientific, E and engineering notation, or do arithmetic on numbers already written as a × 10n.
Enter a regular number, or one already written with e, like 1.5e-7.
Enter X and Y as a number times a power of ten, choose the precision, then press an operation.
Scientific notation writes a number as a value between 1 and 10 multiplied by a power of ten, like 1,568,938 = 1.568938 × 106. It is a tidy way to write numbers that are very large or very small without counting zeros: the mass of the Earth, the width of a hair, the number of molecules in a gram of water. The part before the × is the significand (or mantissa), and the small number above the 10 is the exponent, which tells you how many places the decimal point moved.
The converter gives you the same value in the three styles you will meet. Scientific notation keeps one non-zero digit before the point (1.2345 × 10-4). E-notation is the same thing typed on a keyboard or shown by a calculator or spreadsheet: 1.2345e-4. Engineering notation keeps the exponent a multiple of 3, so the number lines up with units like milli, micro, kilo and mega: 123.45 × 10-6 is 123.45 millionths, which is 123.45 micro-something. The last row converts it all back to an ordinary number.
To add 1.23 × 107 and 3.45 × 102 by hand, first write both with the same exponent: 12,300,000 + 345 = 12,300,345, or 1.2300345 × 107. For multiplication it is easier: multiply the significands and add the exponents. 1.23 × 3.45 = 4.2435 and 7 + 2 = 9, so the product is 4.2435 × 109. For division you divide the significands and subtract the exponents. The calculator does all of this exactly, with no rounding to 15 digits like a typical pocket calculator, and it handles exponents far bigger than a spreadsheet allows.
Addition, subtraction, multiplication, squaring and positive whole-number powers are exact here, so the digits you see are all real. Division, square roots and negative powers can go on forever, so they are cut off (not rounded) after the number of digits after the decimal point set in the precision box. The default of 20 is plenty for homework. If you are doing a lab write-up, remember that the number of significant figures you may quote depends on your measurements, not on the calculator. The Rounding Calculator can round a long result to the figures you need.
In chemistry you will meet Avogadro’s number, 6.022 × 1023, and in astronomy distances like 9.46 × 1015 metres in a light year. If you work with moles and grams, the Molecular Weight Calculator and Molarity Calculator produce values that are often easiest to read this way. Computer storage and network speeds also use powers of ten (and of two), which you can see in the Bandwidth Calculator.
When the digits themselves get long, use the Big Number Calculator, which keeps every digit of huge whole numbers. For exponents and roots of ordinary numbers, the Exponent Calculator and Root Calculator are quicker, and the Log Calculator is the next step if you need to solve for an exponent.
Move the decimal point until there is one non-zero digit in front of it, then multiply by 10 raised to the number of places you moved it. Moving left gives a positive exponent, moving right a negative one.
Scientific notation always has one digit before the point. Engineering notation keeps the exponent a multiple of 3, so the significand can be between 1 and 999.
It stands for "times ten to the power". 1.5E-7 means 1.5 × 10⁻⁷.
Multiply the significands and add the exponents, then adjust so the significand is between 1 and 10.
Addition, subtraction, multiplication and whole-number powers are exact. Division, roots and negative powers are cut off after the number of decimal places in the precision box.
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