Scientific notation

Definition

Scientific notation is a way to express very large or very small numbers as the product of a number between 1 and 10 and a power of 10. It simplifies calculations and comparisons by using exponential form.

5 Must Know Facts For Your Next Test

1. A number in scientific notation is written as $a \times 10^n$, where $1 \leq |a| < 10$.
2. Positive exponents indicate large numbers, while negative exponents indicate small numbers.
3. When multiplying numbers in scientific notation, multiply the coefficients and add the exponents.
4. When dividing numbers in scientific notation, divide the coefficients and subtract the exponents.
5. Standardizing units often involves converting values to scientific notation for easier computation.

Review Questions

• Convert $4500000$ to scientific notation.
• Simplify $(3 \times 10^4) \times (2 \times 10^3)$ using scientific notation.
• Express $5.67 \times 10^{-6}$ in decimal form.

Related terms

Exponent: A number indicating how many times the base is multiplied by itself.

Base: The number that is raised to a power in an exponential expression.

Decimal Notation: A way of writing numbers without using exponents, showing all digits explicitly.