Scientific Notation

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	\(1.0\times 10^{-4}\)