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mathematical Notation

Scientific Notation

The rate of irradiate is around 300,000,000 meters every second. Working v a large number such together this have the right to quickly end up being awkward and cumbersome. To simplify matters, we regularly use scientific notation to stand for very big and very tiny numbers.

Using clinical notation,300,000,000 m/sec can additionally 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 friend see, the larger or the smaller sized the number the an ext beneficial the usage of the clinical notation.

Positive exponents

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

The decimal allude is moved left to just after the very first number. That first number must be at least 1, but less 보다 10. In the instance above, the decimal suggest has been relocated 23 areas to the left. That number is now the confident exponent of the base 10.


Negative exponents

Numbers less than 1 deserve to be expressed in scientific notation by moving the decimal suggest to the right. For example, exactly how would we express 0.0006022?

We still need to follow the convention of clinical notation that the an initial number must be a the very least 1, yet less 보다 10. In this instance, the decimal point needs to relocate to the right by 4 areas to the very first non-zero number. Because that every location we move the decimal to the right we to decrease the strength of ten through one, starting from zero.

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That number have the right to be composed as 6.022 x 10-4 .


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

Set-Builder and also Interval notations