Scientific Notation

Written by Jerry Ratzlaff on . 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  \(\large{ 1 }\)  and  \(\large{ 10 }\) .

  • The number  \(\large{123,000,000 }\)  can be expressed in different ways:
    • \(\large{\;1.23\times 10^8 }\)
    • \(\large{\;1.23\times e^8 }\)
    • \(\large{\;1.23\times e8 }\)
    • \(\large{\;1.23e+8 }\)
    • \(\large{\;123\times 10^6 }\)  engineering notification
     
  • The number  \(\large{0.000000123 }\)  can be expressed in different ways:
    • \(\large{\;1.23\times 10^{-7} }\)
    • \(\large{\;1.23\times e^{-7} }\)
    • \(\large{\;1.23\times e-7 }\)
    • \(\large{\;1.23e-7 }\)
    • \(\large{\;123\times 10^{-6} }\)  engineering notification
     

Multiply:  \(\large{\; \left(3\times 10^8\right) \times \left(2\times 10^4\right) = 6\times 10^{12} }\)

Divide:  \(\large{\; \left(3\times 10^8\right) \div \left(2\times 10^4\right) = 1.5\times 10^4 }\)

 

Number Scientific Notification
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 \(1.0\times 10^{-4}\)