Scientific Notation is a handy way to write very large and very small numbers. Instead of having to use lots of digits, scientific notation allows shorter versions of the number to be written. It uses the format shown below:

m x 10^{n}

where 1 ≤ m < 10

and

n is any integer

Multiplying by a power of ten is a neat, alternate way of writing a number that has many zeros. The table below is a reminder of the value of some powers of ten.

**Powers of 10**

Power | Repeated Multiplication | Value |

10^{2} | 10 x 10 | 100 |

10^{3} | 10 x 10 x 10 | 1,000 |

10^{4} | 10 x 10 x 10 x 10 | 10,000 |

10^{5} | 10 x 10 x 10 x 10 x 10 | 100,000 |

10^{6} | 10 x 10 x 10 x 10 x 10 x 10 | 1,000,000 |

10^{7} | 10 x 10 x 10 x 10 x 10 x 10 x 10 | 10,000,000 |

10^{8} | 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 | 100,000,000 |

**Scientific Notation Examples**

2,300,000 |

can be written as |

2.3 x 1,000,000 |

which can be written as |

2.3 x 10^{6} |

**More Examples**

Number | Scientific Notation |

2,000 | 2 x 10^{3} |

76,000 | 7.6 x 10^{4} |

1,450,000 | 1.45 x 10^{6} |

10,412,000 | 1.0412 x 10^{7} |

909,100,000 | 9.091 x 10^{8} |

4,570,000,000 | 4.57 x 10^{9} |

**Terminology**

**Count the hops!**

Finding the value of the exponent is the main challenge when using scientific notation as this tells us the number that we multiply the co-efficient by. One method to help with this is to think of multiplying by powers of 10 as moving the decimal point – one place for each power of ten. If you think of each move as a hop then you can find what power of ten to multiply the coefficient by. The example below shows that 2.3 multiplied by 10^{6} – six hops – makes 2,300,000.

So, as we have seen above already, 2,300,000 = 2.3 x 10^{6}

**Scientific Notation For Small Numbers**

All the examples above have been of large numbers. Scientific Notation is also very useful for representing very small numbers. In these cases, instead of multiplying, we are in effect dividing by powers of ten. We use negative exponents to show this.

0.000000657 |

can be written as |

6.57 ÷ 10,000,000 |

which can be written as |

6.57 x 10^{-7} |

**More Examples**

Number | Scientific Notation |

0.02 | 2 x 10^{-2} |

0.0021 | 2.1 x 10^{-3} |

0.0000051 | 5.1 x 10^{-6} |

0.00000003 | 3 x 10^{-8} |

Again we can use the “count the hops” method to find the power of ten we are multiplying by (multiplying with a negative exponent has the same effect as dividing)

So 0.00000003 = 3 x 10^{-8}

**Scientific Notation Worksheets**

Try the worksheets below to practice scientific notation..

- Scientific Notation (2-Page Worksheet)