In the field of mathematics, it is recognized as decimal numbers to those that have an integer part, plus a decimal part different from 0. That is, they do not manage to compose an integer. For example: 3 (3/10), 9 (19/10), 1 (1001/10).
Decimal numbers are more difficult to imagine and represent mentally, and in general the only resource that is accepted to understand what they are in fact is to size them as fractions, that is, as whole units divided. However, it can be seen by extension that not all decimal numbers are capable of being expressed as a fraction.
Decimal numbers make up one of the largest groups in the field of number distributions, practically all of them excluding integers and the divisions that can only be made between them: decimals will never be even or odd.
Within this group, for example, appear the:
- exact decimal numbers. Those that have a finite amount of decimals.
- repeating decimal numbers. Those that have an infinite amount, because they come from a division that results in an infinite decimal number, like 1/3.
In another sense, the division appears between the rational decimals (those that can be expressed as a fraction) and the irrational (those that cannot be expressed like this, and have infinite non-periodic numbers, like the famous number pi or the square root of 2).
Expression of decimal numbers
The way to express the decimal numbers, in case you want to show the number and not the fraction, is to place the integer on the left, and after a point the decimal numbers in an ordered manner as if it were a new number.
This has a particularity, since unlike the integers where the neutrality of 0 is to the left, in decimals the neutrality of 0 to the right is assumed: 0.4 is equal to 0.40 and 0.400, and of course greater than 0.39 and 0.399.
If you want to clarify the periodicity of a number, you should place a sign above it or the numbers that you want to show as periodic, and these may not be the end of the decimal figures.
Example list of decimal numbers
The following list includes twenty examples of decimal numbers, accompanied by the irreducible fraction that represents them if they had one.
- 3 (3/10)
- 9 (10/19)
- 1 (1001/10)
- Π (pi number), 3.1415926535…. (not expressible as a fraction)
- 8 (5/14)
- 33 (33/100)
- 75 (883/4)
- 7 (10/37)
- 416666666666666666666 (to infinity) (101/12)
- 5 (3/2)
- 1 (71/100)
- Φ (golden ratio), (1+5^(1/2))/2 (not expressible as a fraction itself, since the root of 5 is also irrational)
- 25 (217/4)
- 333333333333333 (to infinity) (4/3)
- 4 (22/50)
- 9 (59/100)
- 25 (5/4)
- 88888888888888 (to infinity) (71/9)
- 25 (4/13)
- 2^(1/2) (cannot be expressed as a fraction)
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