All positive numbers, all decimal fractions are written in the decimal system. It has only 10 digits:
{0, 1, 2, … 9}
Numbers are few - 10 pieces, and numbers - countless. This is the beauty of the decimal positional system. In it, not only the number itself is important, but also the place (digit) that it occupies.
Example.
Dad gave 300 rubles, mom - 20 rubles, and grandmother - 7 rubles. As a result,
327 = 3∙10 2 + 2∙10 +7.
The fraction 0.327 is written in descending powers of the base.
0,327 = 3∙10 -1 + 2∙10 -2 + 7∙10 -3
So, we remembered the decimal system, in which all positive numbers, all fractions are written in a certain way. So why else do you need a standard form of a number?
To answer this question, consider some large and sufficiently small numbers.
For example, the distance to the Sun is 150,000,000 km.
But it can be written differently - 1.5∙10 8 km. This entry is correct and looks more compact.
The second example would be the diameter of a water molecule (d = 0.0000000003 m)
Let's write it more compactly: d = 3∙10 -10
These are examples of writing a number in standard form. The powers of ten were used here. Before defining the standard form of a number, it is necessary to recall the degrees and operations with degrees.
Definition
The standard form of a positive number "a" is its representation in the form
where a 0 є )
