# Using Scientific Notation

Sometimes, especially when you are using a calculator, you may come up with a very long number. It might be a big number, like 2,890,000,000. Or it might be a small number, like 0.0000073.

**Scientific notation** is a way to make these numbers easier to work with. In scientific notation, you **move the decimal place until you have a number between 1 and 10.** Then you **add a power of ten that tells how many places you moved the decimal.**

In scientific notation, 2,890,000,000 becomes 2.89 x 10^{9}. How?

- Remember that any whole number can be written with a decimal point. For example: 2,890,000,000 = 2,890,000,000.0
- Now, move the decimal place until you have a number between 1 and 10. If you keep moving the decimal point to the left in 2,890,000,000 you will get 2.89.
- Next, count how many places you moved the decimal point. You had to move it 9 places to the left to change 2,890,000,000 to 2.89. You can show that you moved it 9 places to the left by noting that the number should be multiplied by 10
^{9}.

2.89 x 10^{9}= 2.89 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10

2.89 x 10^{9}= 2,890,000,000

Scientific notation can be used to turn 0.0000073 into 7.3 x 10^{-6}.

- First, move the decimal place until you have a number between 1 and 10. If you keep moving the decimal point to the right in 0.0000073 you will get 7.3.
- Next, count how many places you moved the decimal point. You had to move it 6 places to the right to change 0.0000073 to 7.3. You can show that you moved it 6 places to the right by noting that the number should be multiplied by 10
^{-6}.

7.3 x 10^{-6}= 0.0000073

Remember: in a power of ten, the exponent—the small number above and to the right of the 10—tells which way you moved the decimal point.

- A power of ten with a
**positive exponent,**such as 10^{5}, means the decimal was**moved to the left.** - A power of ten with a
**negative exponent,**such as 10^{-5}, means the decimal was**moved to the right.**

Powers of Ten |

billions10 ^{9} = 1,000,000,00010 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000,000 |

millions10 ^{6} = 1,000,00010 x 10 x 10 x 10 x 10 x 10 = 1,000,000 |

hundred thousands10 ^{5} = 100,00010 x 10 x 10 x 10 x 10 = 100,000 |

ten thousands10 ^{4} = 10,00010 x 10 x 10 x 10 = 10,000 |

thousands10 ^{3} = 1,00010 x 10 x 10 = 1,000 |

hundreds10 ^{2} = 10010 x 10 = 100 |

tens10 ^{1} = 10 |

ones10 ^{0} = 1 |

tenths10 ^{–1} = 1/101/10 = 0.1 |

hundredths10 ^{–2} = 1/10^{2}1/10 ^{2} = 0.01 |

thousandths10 ^{–3} = 1/10^{3}1/10 ^{3} = 0.001 |

ten thousandths10 ^{–4} = 1/10^{4}1/10 ^{4} = 0.0001 |

hundred thousandths10 ^{–5} = 1/10^{5}1/10 ^{5} = 0.00001 |

millionths10 ^{–6} = 1/10^{6}1/10 ^{6} = 0.000001 |

billionths10 ^{–9} = 1/10^{9}1/10 ^{9} = 0.000000001 |