a x 10^b
Where:
* a is a number between 1 and 10 (but not including 10). It's called the coefficient.
* 10 is the base, always 10 in scientific notation.
* b is an integer, called the exponent. It indicates how many places the decimal point is moved to the right (if positive) or left (if negative) from the original number.
Here's a breakdown:
* Large numbers: For example, the speed of light is approximately 299,792,458 meters per second. In scientific notation, it's written as 2.99792458 x 10⁸. The decimal point was moved 8 places to the left, making the exponent positive.
* Small numbers: For example, the diameter of a hydrogen atom is approximately 0.0000000001 meters. In scientific notation, it's written as 1 x 10⁻¹⁰. The decimal point was moved 10 places to the right, making the exponent negative.
Benefits of using scientific notation:
* Conciseness: It allows us to express very large or small numbers in a shorter and easier-to-read form.
* Easier manipulation: It simplifies mathematical operations like multiplication and division involving large or small numbers.
* Consistent representation: It provides a standard format for representing numbers across different scientific disciplines.
Examples:
* 1234 = 1.234 x 10³
* 0.0056 = 5.6 x 10⁻³
* 6,000,000,000 = 6 x 10⁹
* 0.000000000000001 = 1 x 10⁻¹⁵
