Scientific Notation

Written by Jerry Ratzlaff. Posted in Algebra

Scientific notation is used to express very large or small numbers rather than having to write out all those zeros. That way we only have to worry about numbers between 1 and 10.

  • The number 123,000,000 can be expressed in different ways:
    • \(1.23\times 10^8\)
    • \(1.23\times e^8\)
    • \(1.23e+8\)
  • Multiplying by 10:
    • \(1.23\times 10^8 = 1.23\times 10\times 10\times 10\times 10\times 10\times 10\times 10\times 10\times = 123,000,000\)
  • Dividing by 10:
    • \(1.23^{-8} = 1.23/10^{-8} = 1.23/100000000 = 0.0000000123\)
NumberScientific

Notation

1 \(1.0\times 10^0\)
10 \(1.0\times 10^1\)
100 \(1.0\times 10^2\)
1,000 \(1.0\times 10^3\)
10,000 \(1.0\times 10^4\)
0.1 \(1.0\times 10^{-1}\)
0.01 \(1.0\times 10^{-2}\)
0.001 \(1.0\times 10^{-3}\)
0.0001 \(1.0\times 10^{-4}\)