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Scientific Notation

The speed of irradiate is approximately 300,000,000 meters per second. Working v a big number such together this deserve to quickly come to be awkward and cumbersome. To leveling matters, we often use scientific notation to stand for very big and very tiny numbers.

Using scientific notation,300,000,000 m/sec can also be composed as

3 x 100,000,000

or in the much shorter form,

3 x 108,

where 8, the exponent, is the number of zeros.

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As you see, the larger or the smaller the number the much more beneficial the usage of the scientific notation.

Positive exponents

Large numbers have the right to be created in scientific notation by relocating the decimal suggest to the left. Because that example, Avogadro"s number is around 602,200,000,000,000,000,000,000 (where the decimal allude implicitly resides to the appropriate of the last zero). Using scientific notation this impressive number is streamlined to: 6.022 x 1023

The decimal point is moved left to just after the very first number. That very first number have to be at least 1, but less than 10. In the instance above, the decimal point has been moved 23 areas to the left. The number is currently the confident exponent the the basic 10.


Negative exponents

Numbers less than 1 have the right to be express in clinical notation by moving the decimal point to the right. For example, exactly how would we express 0.0006022?

We still have to follow the convention of clinical notation the the very first number should be a least 1, however less than 10. In this instance, the decimal suggest needs to move to the appropriate by 4 areas to the first non-zero number. For every location we move the decimal to the right we decrease the power of ten by one, beginning from zero.

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The number can be created as 6.022 x 10-4 .


In the following section we will present set-builder and interval notations.

Set-Builder and also Interval notations