What is Scientific Notation?

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It simplifies the representation of such numbers, making them easier to read, compare, and work with.

A number in scientific notation is written as the product of a number between 1 and 10 and a power of 10. For example, 6,500 can be written as 6.5 × 10³ in scientific notation.

How Does the Conversion Work?

Scientific notation allows us to express numbers in a much more compact form. The process of converting between scientific notation and decimal involves multiplying or dividing by powers of 10.

• Decimal to Scientific Notation: Adjust the decimal point so that the number is between 1 and 10, and then express the number of places the decimal is moved as a power of 10.
• Scientific Notation to Decimal: Move the decimal point to the right for positive exponents and to the left for negative exponents.

Common Uses of Scientific Notation

Scientific notation is widely used in various fields where extremely large or small numbers are common. For example:

• Science & Engineering: Express very large numbers (e.g., distances between stars) or extremely small numbers (e.g., mass of subatomic particles).
• Technology: Represent data sizes, such as memory in bytes, in a concise format.
• Economics & Finance: Simplify the expression of large market values or national GDP figures.

Key Points to Remember

• Exponent Significance: The exponent indicates how many places the decimal point should be moved.
• Precision: Converting to decimal may require rounding to a set number of decimal places.
• Convenience: Scientific notation is used for convenience, though for many numbers within a typical range, decimal form might be more readable.

Examples of Conversion

Here are some examples to illustrate how conversion works between decimal and scientific notation: