Scientific Notation

Scientific Notation is a way to express very small and very large numbers using exponents, and is useful for brevity and for comparing orders of magnitude between numbers.

To convert a number to scientific notation, it is rewritten to be greater than zero but less than ten multiplied by $10$ raised to some exponent.

Simple Examples:

• $99,000$ expressed in scientific notation is $9.9 \cdot 10^4$.
• $0.00099$ expressed in scientific notation is $9.9 \cdot 10^{-4}$

SI number prefixes are commonly used in lieu of scientific or engineering notation. For example, rather than writing "$1.23 \cdot 10^3g$" (grams), we can write "$1.23kg$" (kilograms).

Common large numbers expressed in scientific notation

• Avogadro's number is $6.02214076 \cdot 10^{23}$.
• The charge of an Electron is $0.6021766208 \cdot 10^{-19}$ coulombs.
• A googol is, a one followed by 100 zeros, is $1 \cdot 10^{100}$
• The speed of light is $2.99792458 \cdot 10^8$ meters per second.

Video: Introduction to scientific notation

Deeper Knowledge on Scientific Notation

Engineering Notation

Expressions of very large and very small numbers for engineers

Broader Topics Related to Scientific Notation

Science

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International System of Units (SI)

Formal terms and definitions of the metric system

Math

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