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{{ printedBook.courseTrack.name }} {{ printedBook.name }} **Scientific notation** is a compact way of writing very large or very small numbers. A number written in scientific notation follows the form
$a×10_{b} $
where $1≤a<10$ and $b$ is an integer. For example, the number $4$ million can be rewritten as the product of $4$ and a multiple of $10.$ Then, the multiple of $10$ is rewritten as a base $10$ power.
$4000000=4×1000000=4×10_{6} $
Scientific notation can also be applied to very small decimal numbers, where there are many zeros before the *significant digits*, such as $0.000342.$
$0.000342=3.42÷10000=3.42×10_{-4} $
In such cases, numbers are rewritten as a division by a multiple of $10.$ Division by a multiple of $10$ is equivalent to multiplication by a base $10$ power with negative exponent. Below are a few more examples of numbers written in scientific notation.

Decimal Form | Write as a product or division | Scientific Notation |
---|---|---|

$4505$ | $4.505×1000$ | $4.505×10_{3}$ |

$8320000$ | $8.32×1000000$ | $8.32×10_{6}$ |

$0.0005$ | $5÷10000$ | $5×10_{-4}$ |

$0.0521$ | $5.21÷100$ | $5.21×10_{-2}$ |

An intuitive way to rewrite a number greater than $10$ in scientific notation is done by counting the number of places the decimal needs to move

so the number is greater than or equal to $1$ and less than $10.$ The number of places the decimal moved from right to left indicates the exponent to be used for the base $10$ power.

Similarly, for numbers less than $1,$ such as $0.000022,$ the decimal will move

from left to right. In this case, the number of places moved indicates the negative exponent to be used for the base $10$ power.