# Adding, Subtracting, Dividing, and Multiplying Scientific Notation Calculator 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 to 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.

## Scientific Notation Calculator

Add, subtract, multiply, or divide scientific notation, in any one of three input formats.

Special Instructions

#### Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
1st SN:1st SN:1st scientific notation:Enter first scientific notation:

#### Enter first scientific notation:

Enter the first scientific notation of the equation and then tap the operation (+, −, ×, or ÷) that you wish to perform on the two entries. Note that you can enter scientific notation in any of these formats:
• 35e7
• 35E7
• 35x10^7
 # First scientific notation
2ns SN:2nd SN:2nd scientific notation:Enter second scientific notation:

#### Enter second scientific notation:

Enter the second scientific notation of the equation. Note that you can enter scientific notation in any of these formats:
• 35e7
• 35E7
• 35x10^7
 # Second scientific notation

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.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

#### Related Calculators ## Learn

### 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) ˜ (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

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).

(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 the 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 the 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

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 workarounds to overcome the language's short-comings.

For this reason, the calculator provides two answers: one returned by my workarounds, 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.

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".