Adding, Subtracting, Dividing, and Multiplying
Scientific Notation Calculator

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The Scientific Notation Calculator on this page will add, subtract, divide, or multiply power of 10 notations.

This free online calculator will perform addition, subtraction, division, or multiplication on two given scientific notations (SN, also referred to as exponential notation).

Plus, unlike other online SN 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 SN is, or you would like to learn how convert SN to or from regular notation, please visit the Scientific Notation Converter located in the Conversion Calculators section. Knowing how to convert back and forth will be necessary to understand the operations explained on this page.

Scientific Notation Math

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.

Multiplying Scientific Notation

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).

Example multiplication problem: (3 x 106) x (6 x 104)

Here are the steps to solving the above problem.

Multiplication Steps (3 x 106) x (6 x 104)
Group like terms: = (3 x 6) x (106 x 104)
Multiply coefficients and add exponents: = (18) x (1010)
Convert to proper SN: = 1.8 x 1011

The other way to multiply scientific notations is to convert the notations to real numbers, perform the multiplication, and then convert the number back to scientific notation, like the following:

Alternative Multiplication Method
(3 x 106) x (6 x 104)
= (3 x 1000000) x (6 x 10000)
= 3000000 x 60000
= 180000000000
= 1.8 x 1011

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.

Dividing Scientific 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).

Example division problem: (5 x 108) ÷ (2 x 104)

Here are the steps to solving the above problem.

Division Steps (5 x 108) รท (2 x 104)
Group like terms: = (5 ÷ 2) x (108 ÷ 104)
Divide coefficients and Subtract exponents: = (2.5) x (104)
Convert to proper SN: = 2.5 x 104

The other way to divide scientific notations is to convert the notations to real numbers, perform the division, and then convert the number back to scientific notation, like the following:

Alternative Division Method
(5 x 108) ÷ (2 x 104)
= (5 x 100000000) ÷ (2 x 10000)
= 500000000 ÷ 20000
= 25000
= 2.5 x 104

Adding Scientific Notation

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).

Example addition problem: (6 x 104) + (7 x 103)

Here are the steps I use to solve the above addition problem.

Addition Steps (6 x 104) + (7 x 103)
Factor out 1 of the powers of 10 = (6 x 104/104 + 7 x 103/104) x 104
Perform division of exponents: = (6 x 100 + 7 x 10-1) x 104
Convert SN's to real numbers: = (6 + 0.7) x 104
Combine real numbers: = (6.7) x (104)
Convert to proper SN: = 6.7 x 104

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.

Addition Steps (6 x 104) + (7 x 103)
Convert numbers to same exponents: = (6 x 104) + (.7 x 104)
Add coefficients and keep the exponent the same: = (6.7 x 104)
Convert to proper SN: = 6.7 x 104

A third way to add scientific notations (if the numbers aren't too large or small) is to convert the notations to real numbers, perform the addition, and then convert the number back to scientific notation, like the following:

Alternative Addition Method
(6 x 104) + (7 x 103)
= (6 x 10000) + (7 x 1000)
= 60000 + 7000
= 67000
= 6.7 x 104

Subtracting Scientific Notation

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).

Example subtraction problem: (7 x 106) - (4 x 103)

Here are the steps I use to solve the above subtraction problem.

Subtraction Steps (7 x 106) - (4 x 103)
Factor out 1 of the powers of 10 = (7 x 106/106 - 4 x 103/106) x 106
Perform division of exponents: = (7 x 100 - 4 x 10-3) x 106
Convert SN's to real numbers: = (7 - 0.004) x 106
Perform real number subtraction: = (6.996) x (106)
Convert to proper SN: = 6.996 x 106

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.

Addition Steps (7 x 106) - (4 x 103)
Convert numbers to same exponents: = (7 x 106) - (.004 x 106)
Subtract coefficients and keep the exponent the same: = (6.996 x 106)
Convert to proper SN: = 6.996 x 106

The third way to subtract one scientific notation from another (if numbers aren't too large or small) is to convert the notations to real numbers, perform the subtraction, and then convert the number back to scientific notation, like the following:

Alternative Subtraction Method
(7 x 106) - (4 x 103)
= (7 x 1000000) - (4 x 1000)
= 7000000 - 4000
= 6996000
= 6.996 x 106

Double Check the Answer

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 let me know the notations you entered and the operation you selected so I can investigate the difference.

With that, let's use the Scientific Notation Calculator to add, subtract, divide, or multiply exponential notations.

Scientific Notation Calculator
Calcy sign introducing Scientific Notation Calculator


Instructions: Enter a scientific notation the first line, choose the operation to perform, enter a second scientific notation on the third line, and then click the "Perform Scientific Notation Math" button.

Note that when entering a scientific notation you can enter it in any one of three acceptable formats: 2.4e-5, 2.4E-5, or 2.4 x 10^-5 (the "^" can be entered by pressing the 6 key while holding down the shift key on most keyboards). Regardless of which format you choose to use, the calculator will display the results in latter format.

Mouse over the blue question marks for a further explanation of each entry field. More in-depth explanations can be found in the glossary of terms located beneath the Scientific Notation Calculator.

Help Enter first scientific notation:
Help Choose operation:
Help Enter second scientific notation:
Help Answer:
Help Raw answer:

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Scientific Notation Calculator Glossary of Terms

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Enter first scientific notation: Enter a scientific notation any of these formats: 35e7, 35E7, or 35x10^7.

Choose operation: Choose the operation you would like the calculator to perform on the two entered exponential notations (plus, minus, times, or divided by).

Enter second scientific notation: Enter a scientific notation in any of these formats: 35e7, 35E7, or 35x10^7.

Answer: This is the result achieved by performing the selected operation on the two entered notations.

Raw answer: This is the answer as returned by the programming language this calculator is created in -- which may or may not return a scientific notation, and/or an oddly rounded decimal. I provide the raw answer so you can compare it to the answer I came up with by manipulating text strings instead of calculating with numbers. If the two answers are different beyond just rounding differences, please let me know the notations you entered and the operation you selected so I can investigate the matter.

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