What is the scientific notation?

The scientific notation is used when we want to express very big numbers or very small numbers. Let’s suppose we want to calculate the distance, in metres, from the Planet Earth to the Sun. The result of this calculation consists in a very big number which is difficult not only to write but also to read! The same happens if you want to calculate the weight of one atom in grams. To do so it would be necessary a very small number! And then, once again, it becomes difficult to use the conventional pattern to which we are used to.

Every number, according to scientific notation, means `mxx10^n`. Letter `m` stands for mantissa and it will have to a number whose absolute value is between 1 and 10. Concerning letter `n` it represents the order of magnitude and must be a whole number.

Could you give some examples of scientific notation numbers?

• Mass of the Earth: `5.973.600.000.000.000.000.000.000` kg. Scientific Notation: `5,9736xx10^24` kg.
• Mass of an electron: `0,000.000.000.000.000.000.000.000.000.000.9` kg. Scientific Notation: ` 9xx10^-31` kg.

What are the advantages of this format?

Besides allowing the representation of extremely big and small numbers according to a more abridged way, the scientific notation also has the advantage of allowing an easy comparison concerning the order of magnitude between two numbers. Besides that, the calculations required by the four basic arithmetic operations (addition, subtraction, multiplication and division), are also much more easy to perform when the numbers are according to this format.

When did the scientific notation appear?

Archimedes was the Greek philosopher and mathematician who supposedly made the first attempt to use scientific notation numbers. By the 3rd century B.C he needed to use them when he made an estimate to calculate the necessary number of sand grains to fill the Universe. The number he estimated corresponded to `1xx10^63` grains.

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