Scientific Notation Formula

Scientific notation is a way to write very large or very small numbers in a shorter and easier form. It is commonly used in science, mathematics, and engineering.

Scientific Notation Formula

The standard form of scientific notation is:

a × 10n

Here, a is a number greater than or equal to 1 and less than 10, while n is an integer that shows how many places the decimal point has moved.

Converting a Large Number

To write a large number in scientific notation, move the decimal point to the left until only one non-zero digit remains before it.

For example:

450,000 = 4.5 × 105

The decimal point moves 5 places to the left, so the exponent is 5.

Converting a Small Number

For a number smaller than 1, move the decimal point to the right. The exponent becomes negative.

For example:

0.00072 = 7.2 × 10−4

The decimal point moves 4 places to the right, so the exponent is −4.

Multiplying Numbers in Scientific Notation

To multiply numbers in scientific notation, multiply the coefficients and add their exponents.

(2 × 103)(4 × 102) = 8 × 105

Dividing Numbers in Scientific Notation

To divide numbers in scientific notation, divide the coefficients and subtract the exponent of the denominator from the exponent of the numerator.

(8 × 106) ÷ (2 × 102) = 4 × 104