Scientific Notation Calculator

The scientific notation calculator is used to add, subtract, multiply, and divide two scientific notation numbers.

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How to Use the Scientific Notation Calculator?

  1. Firstly, input the coefficient and exponent values for the first and second numbers.
  2. Select the arithmetic operation that you want to perform between two numbers. The tool supports addition, subtraction, multiplication, and division.
  3. After inputting all the values, press the 'Calculate' button.
  4. The tool returns the scientific notation, E notation, and decimal notation results on your screen.
  5. For the new calculations, press the 'Reset' button. It will make all the fields empty.

What is Scientific Notation?

The scientific notation is used to express very large or small numbers in a simple form. It makes the numbers easier to read, compare, and work with. It uses the powers of ten to simplify the numbers.

The general form of a number in scientific notation is:

b × 10n

Where,
b = Coefficient,
n = Exponent.

The scientific notations are widely used in the science, mathematics, physics, chemistry, engineering, and many more fields.

Example:

The speed of the light is 299792458 m/s.

It's hard to remember and complex for the math calculations.

So, it can be written in scientific notation as 2.99 × 108 m/s.

Calculations with Scientific Notation

Let's learn how to perform basic arithmetic calculations with scientific notation.

1. Addition and Subtraction

The exponent values must be the same to perform addition or subtraction in scientific notation. If it's not, adjust any one number.

Example:

( 3 × 105 ) + ( 0.5 × 106 )

Solution:

First, make the exponent same for both values.

So, convert 0.5 × 106 to 5 × 105.

Now, add the coefficients and combine the results.

( 3 × 105 ) + ( 5 × 105 ) = 8 × 105.

Let's take an example of subtraction.

Example:

( 6 × 104 ) - ( 2 × 105 )

Solution:

2 × 105 can be written as 20 × 104.

Now, the exponents are the same for both values. So, subtract the coefficients and combine the results.

( 6 × 104 ) - ( 20 × 104 ) = -14 × 104

= -1.4 × 105

3. Multiplication

In multiplication, multiply the coefficient values and add the exponents.

( a × 10m ) × ( b × 10n ) = ( a × b ) × 10 m + n

Let's take an example.

Example:

( 5.4 × 107 ) × ( 8.7 × 105 )

Solution:

1. Multiply the coefficients: 5.4 × 8.7 = 46.98

2. Add the exponents: 7 + 5 = 12

3. Combine the results: 46.98 × 1012

Also, it can be written as: 4.698 × 1013.

4. Division

In division, divide the coefficients and subtract the exponents.

( a × 10m ) / ( b × 10n )

= ( a / b ) × 10 m - n

Example:

( 24 × 106 ) / ( 3 × 102 )

Solution:

1. Divide the coefficient values: 24 / 3 = 8.

2. Subtract the exponents: 6 - 2 = 4.

So, the final result is 8 × 104.