Scientific Notation Calculator

What this calculator does

So, you have two numbers written in scientific notation and you want to add, subtract, multiply, or divide them. This tool does the arithmetic. Enter the two numbers, choose an operation, and it gives you the result.

It reads numbers written with the e-notation shorthand, so very large and very small values are easy to enter.

How to use it

1. Enter Number A, in scientific notation or as a plain number.
2. Choose the operation: add, subtract, multiply, or divide.
3. Enter Number B, then press Calculate.

What scientific notation is

Scientific notation is a compact way of writing numbers that are very large or very small. Instead of writing out a long string of zeros, you write the number as a value between 1 and 10 multiplied by a power of 10. So 300,000 becomes 3 times 10 to the power 5, and 0.0002 becomes 2 times 10 to the power minus 4. The power of 10 records the order of magnitude, how many places the decimal point has shifted. This keeps huge and tiny numbers readable, which is why science and engineering lean on it so heavily.

How to type it in

On a keyboard, the times 10 to a power part is usually written with the letter e, which stands for exponent. So 3 times 10 to the power 5 is typed as 3e5, and 1.1 times 10 to the power minus 7 is typed as 1.1e-7. A capital E works just as well. This tool understands that shorthand, so you can enter numbers in the same form your calculator or spreadsheet would use. You can also just type an ordinary number like 6.78 if that is easier; the tool handles both.

The four operations

The tool offers the four basic arithmetic operations from a dropdown: addition, subtraction, multiplication, and division. Whichever you choose, it takes your two numbers, works out the operation, and shows the result. Behind the scenes it reads each number, including its power of 10, converts it to a plain value, and combines the two. This means you do not have to line up the exponents by hand or juggle the powers of 10 yourself, which is exactly the fiddly part of doing scientific-notation arithmetic on paper.

A worked example

Suppose you enter 3e5 and 2e5 and choose addition. The tool reads these as 300,000 and 200,000, adds them, and returns 500,000. Now try multiplication with 4e3 and 2e2: those are 4,000 and 200, and multiplying them gives 800,000. Notice how the tool lets you enter the numbers in their short powers-of-ten form while it takes care of combining them.

Why calculate this way

Working in scientific notation is not just tidier, it is often the only sensible way to handle the numbers that turn up in real problems. Distances between stars, the size of an atom, populations, and data volumes all run to many digits, and writing them out in full invites mistakes with miscounted zeros. Scientific notation keeps the significant part of the number separate from its scale, so the arithmetic stays manageable. If instead you have an ordinary number and want to convert it into this form, the standard form calculator writes any number as a value times a power of 10.

Questions people ask

What is scientific notation?

A way of writing a number as a value between 1 and 10 times a power of 10, such as 3 times 10 to the power 5 for 300,000.

How do I type a power of 10?

Use the letter e for the exponent. So 3e5 means 3 times 10 to the power 5, and 1.1e-7 means 1.1 times 10 to the power minus 7.

What operations can it do?

Addition, subtraction, multiplication, and division of the two numbers you enter.

Can I enter ordinary numbers too?

Yes. A plain number like 6.78 works just as well as one in scientific notation.

How do I convert a number into scientific notation?

Use the standard form calculator, which rewrites any number as a value times a power of 10.

References

On scientific notation. A number is written in scientific notation as a value between 1 and 10 multiplied by a power of 10.

1. Christopher Stover and Eric W. Weisstein, "Scientific Notation," from MathWorld, a Wolfram resource, on writing a number in the form a times 10 to a power.
2. Lynda Sherman and Eric W. Weisstein, "Arithmetic," from MathWorld, a Wolfram resource, on the operations of addition, subtraction, multiplication, and division.