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 1010 raised to some exponent.

Simple Examples:

  • 99,00099,000 expressed in scientific notation is 9.91049.9 \cdot 10^4.
  • 0.000990.00099 expressed in scientific notation is 9.91049.9 \cdot 10^{-4}

SI number prefixes are commonly used in lieu of scientific or engineering notation. For example, rather than writing "1.23103g1.23 \cdot 10^3g" (grams), we can write "1.23kg1.23kg" (kilograms).

Common large numbers expressed in scientific notation

  • Avogadro's number is 6.0221407610236.02214076 \cdot 10^{23}.
  • The charge of an Electron is 0.602176620810190.6021766208 \cdot 10^{-19} coulombs.
  • A googol is, a one followed by 100 zeros, is 1101001 \cdot 10^{100}
  • The speed of light is 2.997924581082.99792458 \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


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International System of Units (SI)

Formal terms and definitions of the metric system


Fun with numbers

Scientific Notation Knowledge Graph