Scientific Notation Formula

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56 × 10⁷. It is a form of presenting very large numbers or very small numbers in a simpler form. The scientific notation helps us to represent the numbers that are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small. Let's understand the scientific notation formula.

What is Scientific Notation Formula?

A scientific notation is a form of writing a given number, an equation, or an expression in a form that follows certain rules. Writing a large number like 8.6 billion in its number form is not just ambiguous but also time-consuming and there are chances that we may write a few zeros less or more while writing in the number form. So, to represent very large or very small numbers concisely, we use scientific notation. The general representation of scientific notation or scientific notation formula is given as:

a × 10^b ; 1 ≤ a < 10

'a' represents any number between 0 to 10 ( greater than 0 and lesser than 10)where, 

Scientific Notation Rules

To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.

• If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive.

           Example: 8000 = 8 × 10³ is in scientific notation.

• If the given number is smaller than 1, then the decimal point has to move to the right, so the power of 10 will be negative.

           Example: 0.0005 = 5 × 0.0001 = 5 × 10^-4 is in scientific notation.

Positive and Negative Exponent

• When the scientific notation of any large numbers is expressed, then we use positive exponents for base 10.

            Example: 5000000 = 5 x 10⁶, where 6 is the positive exponent.

• When the scientific notation of any small numbers is expressed, then we use negative exponents for base 10. 

            Example: 0.00004 = 4 x 10^-5, where -5 is the negative exponent.

Let us see the applications of the scientific notation formula in the following solved examples.

Solved Examples Using Scientific Notation Formula

Example 1: Convert 0.00000084 into scientific notation using scientific notation formula.

Solution: 

Move the decimal point to the right of 0.000000084 up to 8 places.

The decimal point was moved 8 places to the right to form the number 8.4

Since the numbers are less than 10 and the decimal is moved to the right, so we use a negative exponent here.

⇒ 0.000000084 = 8.4 × 10^-8

Answer: Thus, in scientific notation 0.000000084 is expressed as 8.4 × 10^-8

Example 2: Can you help Zoe to write \(7.56\times10^{11}\) in the standard notation?

Solution

Here, \(7.56\) is \(756\). Now, Zoe has to move the decimal point 11 places to the right and add zeroes accordingly.

The standard notation for \(7.56\times10^{11}\) is \(756,000,000,000\). 

Answer: Thus, the standard form is 756,000,000,000.​​​​​​