Scientific Notation Calculator

Scientific Notation Calculator helps you to add, subtract, multiply, and divide any two standard forms of numbers instantly.

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About Scientific Notation Calculator

Are you having trouble dealing with the mathematical calculations involving Scientific Notations? No more! Our online Scientific Notation Calculator makes this job easy, fast, and accurate.

Also, you can add, subtract, multiply, and divide any two scientific or standard forms of numbers.

Scientific Notation Calculator

What is Scientific Notation?

Scientific Notations are used for representing very large or very small numbers. Like Nano, Micro, Trillion, and Pico. Also, it is very useful as it makes the calculations convenient when operating with small decimals rather than using long floating-point numbers.

Scientific Notation represents a coefficient multiplied by 10 to the nth power.

We can define it as:

b × 10n

Some examples are as follows:

  • 1.3 × 107
  • 8.12 × 10-41
  • 6 × 103

The value present on the left side is called the "mantissa". It is the coefficient and the highest significant value. Also, it can vary according to the significant values present in the number. The value present on the right side is the "multiplicative factor".

Computer systems also take a much longer time to compute results with long floating-point numbers. Using scientific notations, we can make the calculations easier and faster.

Even more, in real life, it becomes much easier to perform calculations with decimals as compared to floating-point numbers. If you have got a very long or very short number then it should be converted into a standard form or scientific notation form. Scientific Notation Calculator will help you achieve it.

Basic Rules for Scientific Notation

There are some basic rules governing the conversion of a number to scientific notation form. Let's learn about them so that we can accurately perform the conversion.

  1. Make sure the decimal in the number should be in between the first two numbers and those are not equal to zero.
  2. The number before the multiplication symbol is called "mantissa". It is the highest significant value.
  3. The total number of digits represents the significant figures.
  4. The value of the exponent determines the position of the decimal in the original number. If we move the decimal to the right side then the exponent will be negative. Similarly, if we move the decimal to the left side then the exponent will be positive.

How Scientific Notation Calculator Works?

Here, we will explain how the mathematical calculations take place inside our calculator. Also, the procedures for these calculations are different from the normal arithmetic calculations. Let's have a look one by one.

1. Addition

In addition, firstly, we need to convert all the numbers into the same power of 10. Then simply add the significant values to get the final result.

Example:

( 3 × 105 ) + ( 0.5 × 106 )

Solution:

Firstly, we need to bring both the values to the same power of 10.

So, we can write 0.5 × 106 as 5 × 105.

Now both the values are of the same power of 10. So, we will simply add them.

( 3 × 105 ) + ( 5 × 105 ) = 8 × 105

2. Subtraction

Subtraction also used the same procedure that was followed in addition. Firstly, we will equalize all the power of 10 and then subtract both values.

Example:

( 6 × 104 ) - ( 2 × 105 )

Solution:

2 × 105 can be written as 20 × 104.

As we can see, the power of 10 is the same in both values. So, now we will simply find the difference between them.

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

= -1.4 × 105

3. Multiplication

In multiplication, the digits on the left side (mantissa) are multiplied and added the exponent values. Let's see an example.

Example:

( 5.4 × 107 ) × ( 8.7 × 105 )

Solution:

Firstly, we will multiply 5.4 with 8.7.

5.4 × 8.7 = 46.98

Secondly, we will add the exponent (7 and 5) values.

7 + 5 = 12

The final result will be: 46.98 × 1012.

Also, we can write this as: 4.698 × 1013.

4. Division

In division, the digits on the left side (mantissa) are divided and the exponents are subtracted. Let's understand it with an example.

Example:

( 24 × 106 ) / ( 6 × 102 )

Solution:

Firstly, we will divide the significant digits. Those are 24 and 6.

So, 24 / 6 = 4

After that, we will subtract the exponent (6 and 2) values.

6 - 2 = 4

So, our final result is: 4 × 104.

Applications

As the name signifies, scientific notations are widely used in the field of science. Most importantly, it is basically used in mathematics, physics, engineering formulas, chemistry, scientific equations, accountancy, etc.

Example 1:

The speed of the light is 299792458 m/s.

It's hard to remember and use in mathematical equations.

Therefore, we will round off it and represent it in scientific notation as 2.99 × 108 m/s.

More conveniently, we can write it as 3 × 108 m/s.

Features of Scientific Notation Calculator

  • Amazingly fast: Our tool is very fast when it comes to finding results.
  • Multiple operations supported: It supports all the basic mathematical operations. So, you can use it for addition, subtraction, multiplication, and division.
  • Multiple result format: Our calculator displays the result in three forms: Scientific Notation, E Notation, and Decimal Notation.
  • Simplified user interface: Using the tool is very easy because of the minimalistic and efficient design. Even more, you will get your answer in just a few simple steps.
  • Free unlimited usage: You can use the calculator as many times as you want for absolutely free. No hidden charges or anything. It's totally free forever.

How to use Scientific Notation Calculator?

Follow these simple steps to perform arithmetic operations between the two standard forms of numbers.

  1. Firstly, open the Scientific Notation Calculator in your web browser.
  2. You can see some input boxes. So, fill in the values respectively for both the operands. Write the significant values into the first box. Whereas write the exponent value will into the box that is above 10.
  3. After that, just select the arithmetic operation from the drop-down that you want to perform. Our tool supports addition, subtraction, multiplication, and division.
  4. After selecting the operation, just press the "Calculate" button. As a result, you will get the output in three forms. Scientific Notation, E Notation, and Decimal Notation.
  5. For a new calculation, just use the Reset button. It will make all the fields empty.

Frequently Asked Questions

Standard Form and Scientific Notation both are the same things with different names. Scientific Notation is referred to as Standard Form in Britain.

There is no limit for maximum or minimum values. You can write any numerical value.

Yes, the tool supports negative and decimal values in both significant and exponent.

You can perform Addition, Subtraction, Multiplication, and Division.