Scientific notation

Definition

Scientific notation is a way of expressing very large or very small numbers in the form $a \times 10^n$, where $1 \leq a < 10$ and $n$ is an integer. It simplifies calculations and representation of numbers by using powers of ten.

5 Must Know Facts For Your Next Test

1. In scientific notation, the coefficient $a$ must be between 1 and 10, including 1 but not 10.
2. The exponent $n$ indicates how many places the decimal point has been moved to convert the number to standard form.
3. A positive exponent means the decimal point is moved to the right, while a negative exponent means it is moved to the left.
4. Scientific notation helps in comparing orders of magnitude more easily.
5. $2.5 \times 10^3 = 2500$ demonstrates how scientific notation can simplify multiplication and division operations.

Review Questions

• How would you express the number $0.00045$ in scientific notation?
• What does a negative exponent signify in scientific notation?
• $7.89 \times 10^5$ represents which standard form number?

Related terms

Exponent:

An exponent refers to the number that indicates how many times a base is multiplied by itself.

Standard Form:

The normal way of writing numbers without exponents, also known as decimal or regular form.

Order of Magnitude:

A class in a system for classifying numbers according to size, usually based on powers of ten.