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

Math

Fun with numbers

Science

The most rigorous system of epistemology

International System of Units (SI)

Formal terms and definitions of the metric system

Scientific Notation Knowledge Graph