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Scientific Notation

The speed of irradiate is approximately 300,000,000 meters per second. Working with a huge number such as this can quickly come to be awkward and cumbersome. To simplify matters, we often use scientific notation to represent very big and very tiny numbers.

Using scientific notation,300,000,000 m/sec can likewise be created as

3 x 100,000,000

or in the 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 more beneficial the use of the scientific notation.

Positive exponents

Large numbers have the right to be created in scientific notation by moving the decimal suggest to the left. For example, Avogadro"s number is around 602,200,000,000,000,000,000,000 (where the decimal point implicitly lives to the appropriate of the last zero). Using clinical notation this outstanding number is simplified to: 6.022 x 1023

The decimal point is moved left to just after the an initial number. That first number must be at the very least 1, but less than 10. In the example above, the decimal allude has been relocated 23 places to the left. The number is now the optimistic exponent the the base 10.


Negative exponents

Numbers less than 1 can be to express in clinical notation by moving the decimal suggest to the right. Because that example, exactly how would we express 0.0006022?

We still have to follow the convention of scientific notation that the very first number must be a the very least 1, but less than 10. In this instance, the decimal suggest needs to move to the right by 4 locations to the an initial non-zero number. Because that every ar we move the decimal come the right we to decrease the power of ten by one, starting from zero.

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The number deserve to be created as 6.022 x 10-4 .


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

Set-Builder and also Interval symbol