This is the result achieved by performing the selected operation on the two entered notations.
This is the answer as returned by the programming language this calculator is created in -- which may return a scientific notation, and/or an oddly rounded result. I provide it so you can compare it to the answer I came up with by manipulating text strings instead of calculating with numbers.
This calculator will perform addition, subtraction, division, or multiplication on two given scientific notations (SN, also referred to as exponential notation).
Plus, unlike other similar online calculators, this calculator will not only display the steps it used to perform the selected scientific notation math, but it will also show how the answer could be arrived at manually.
Note that if you don't know what scientific notation is, or you would like to learn how convert scientific notation to or from regular notation, please visit the Scientific Notation Converter located on the full site. Knowing how to convert back and forth will be necessary to understand the operations explained on this page.
Enter the first exponential notation.
Enter the second exponential notation.
Click the "Perform SN Math" button. This will display the result of the operation performed on the two entries, plus display the raw answer, a chart showing the steps the calculator took to solve the equation, and a chart showing how to check the answer manually.
Since it's important that you know how to perform scientific notation math without requiring a calculator -- especially if you may be required to show your work -- I have included a short lesson for each operation on this page. Note that each lesson is reflective of the results that will appear in the calculated results.
To multiply two SN's you basically just multiply the coefficients and add the exponents, and then convert that result to proper scientific notation format (if not already).
Here are the steps to solving the above problem.
Of course, this alternative method can be cumbersome if the numbers you are working with are very large or very small, and may not be possible if the calculator you are using won't display the results in regular notation.
To divide two SN's you divide the coefficients and subtract the trailing exponent from the leading exponent, and then convert that result to proper scientific notation format (if not already).
To add two SN's you factor out one of the powers of 10, convert the remaining scientific notations to real numbers, add the real numbers, and then convert that result to proper scientific notation format (if not already).
Here are the steps I use to solve the above addition problem.
There is a second method for solving the above addition problem (not included in the calculated results), which requires converting the numbers to the same power of 10. To do that you move the decimal point of one coefficient to left or right the number of places needed to make that number's power of 10 equal to the other. You then add the resulting coefficients while keeping the power of 10 the same.
To subtract one SN from another, you first factor out one of the powers of 10, convert the remaining scientific notations to real numbers, subtract the second real number from the first, and then convert that result to proper scientific notation format (if not already).
Here are the steps I use to solve the above subtraction problem.
There is a second method for solving the above subtraction problem (not included in the calculated results), which requires converting the numbers to the same power of 10. To do that you move the decimal point of one coefficient to left or right the number of places needed to make that number's power of 10 equal to the other. You then subtract the resulting coefficients while keeping the power of 10 the same.
Since the programming language I use to create online calculators is not well-equipped to handle very large or very small numbers, I had to come up with several bizarre work-arounds to overcome the language's short-comings.
For this reason the calculator provides two answers: one returned by my work-arounds, and one returned by the programming language. If these two answers are different beyond just rounding issues, please use the feedback form beneath the calculator to let me know the notations you entered and the operation you selected so I can investigate the difference.