Multiplying Scientific Notation Calculator

If you've ever wondered how to find the product of two numbers written in scientific notation, you've come to the right place with our multiplying scientific notation calculator. We know multiplying in scientific notation can be intimidating, but don't worry! We've created a straightforward and user-friendly tool to make it less so.

Keep reading and discover:

• What is scientific notation;
• How to write in scientific notation;
• How to use our scientific notation multiplication calculator; and
• How to multiply scientific notations without a multiplying scientific notation calculator.

Try it now and discover that multiplying in scientific notation is actually not rocket science!

Scientific notation is a more practical way of expressing numbers. It enables computers or calculators to display the value of a very large or very small number as a × 10ⁿ. This notation is made up of 2 parts:

• A decimal number, a, between 0 and 10 (excluded), called the "mantissa"; and
• A power of 10, i.e., the product of 10 times itself as many times as the exponent, n.

For example: 3.11 × 10⁻⁹ or 7.005 × 10¹³ are numbers written in scientific notation.

If you want to convert a number to scientific notation quickly, check out our scientific notation converter.

Take, for example, the speed of light in a vacuum. It is 299,792,458 m⋅s⁻¹.

We know that writing this number in scientific notation means writing it as a decimal whose integer part is between 1 and 9 multiplied by a power of 10.

1. First of all, we can say that this number, 299,792,458, is a decimal multiplied by 10⁰ (which is 1), so we can write it as 299,792,458 × 10⁰.

2. Then, to convert this value to scientific notation, divide the decimal part, 299,792,458, by one hundred million (10⁸) to obtain a number between 1 and 9. The result is 2.99792458

3. At the same time, multiply the "power of 10" part by 10⁸ so that the product of the decimal part and the power of 10 gives the same final value.

4. The scientific notation of 299,792,458 will therefore be 2.99792458 × 10⁸.

   This number has 9 significant figures. We sometimes see people rounding this number to 1 significant figure, i.e., 3.0 × 10⁸ m⋅s⁻¹. If rounding numbers is not your thing, you can always use our rounding calculator for accurate results.

So, to sum up, we've moved the decimal point (initially after the last digit 8) to 8 rows to place it after the 2. And we've multiplied by 10⁸.

Using our multiplying scientific notation calculator is very simple. Suppose you want to calculate 9.876 × 10³ multiplied by 5.432 × 10⁻².

1. In the first field Number 1 enter 9.876, then use the drop-down menu to find 10³. Do the same for the second number. Enter 5.432 in the field Number 2 below and select 10⁻² from the drop-down menu.

2. Next, you can adjust the number of significant figures. The default value is 10.

3. Finally, the result will appear at the bottom of our scientific notation multiplication calculator:

   • Scientific notation: 5.3646432 × 10²
   • e-notation:  5.3646432e2
   • Decimal notation: 536.46432

After reading the last section, we're sure you are wondering… But how do I multiply scientific notations without a calculator? Good question! Well, as with everything that has to do with scientific notation, it is pretty simple.

Let's say you have two numbers written in scientific notation: a × 10ⁿ and b × 10^m. To multiply them, multiply the coefficients and add the exponents: (a × b) × 10^n+m.

Suppose your two numbers are 3.2 × 10² and 1.4 × 10⁻³. It gives us:

(3.2 × 1.4) × 10²⁺⁽⁻³⁾ = 4.48 × 10⁻¹

Don't forget to check this result with our multiplying scientific notation calculator.