1. Non-integer numbers that are used to represent the fractional part of an integer, that is, they are numerical sequences expressed from the separation by a comma to the left of the numerator in a scale of tens. Examples: A)’ 0.02 = 2/100′. B) ‘54.5 = 54 and 5/10’.
Grammatical category: masculine noun
in syllables: numbers + decimals.
Decimal numbers
Evelyn Maitee Marin
Industrial Engineer, MSc in Physics, and EdD
Decimal numbers are made up of figures that contain an integer part, followed by a period, and then a decimal part. They are used to express values that are between two consecutive integers.
Between two integers, there are infinitely many decimal numbers that can be represented on a number line.
Although there is no precise date of invention of decimal numbers, the records of their first uses in the West are attributed to Simon Stevin in 1585, who used them as an alternative to the use of fractions. However, the way of expressing decimal numbers at that time differs from the current one, for example, to represent the number 0.0796; I stated it this way:
which reads: 7 seconds, 9 thirds, 6 fourths.
The nomenclature used today was proposed by John Napier, in which a decimal point (or a comma) is used for decimal numbers, in the same way as it is used today.
Decimal numbers belong to the set of rational numbers (Q) and irrational numbers (I)
Place value
Place value relates to the location each digit occupies in a number. In particular, decimal numbers obey two types of positions: one for the integer part, and another for the decimal part, since they are represented as follows:
As can be seen, the point in a decimal number is the symbol that separates the integer part (on the left) from the decimal part (right side).
However, depending on the location that each digit occupies in the figure, a positional value is associated with it considering the following categories:
types of decimal numbers
exact decimals: This denomination is used to refer to decimal figures made up of a finite or limited number of digits, for example:
– 1,907 (contains decimals up to the thousandth)
– 158621.03348 (contains decimals up to one hundred thousandth)
– 847.9 (contains decimals up to the tenth)
periodic numbers: unlike exact decimals, in this category are decimal figures that have infinitely many digits in their decimal part and this exhibits a repeating pattern. The periodic numbers can be classified in turn into:
pure newspapers: These numbers have a decimal part that is repeated immediately after the decimal point. By convention, in the decimal number pattern, an arc is usually placed at the top, so for example, the number 1.33333333… can be expressed:
mixed newspapers: these numbers have in their decimal part one or more digits that precede the periodic numbers, so the numbers of the decimal figure that precede the period are called before – period, for example, in the number 36.07999999…, it can be identify:
Not exact or periodic
These decimal numbers have infinitely many non-recurring digits in their decimal part, and are also known as irrational numbers; that is, they do not have patterns in the decimal part which contains infinitely many digits, for example:
The result of π (pi) represents a decimal number, since it contains infinite non-recurring digits in its decimal part, therefore, it belongs to the set of irrational numbers. The value of π is a constant that is determined by dividing the perimeter of any circle by its diameter. In many contexts its decimal part is approximated to the hundredth π = 3.14
Transformation of a decimal number into a fraction
Any exact or repeating decimal number can be converted to an equivalent fraction. The procedure for said transformation is:
For exact decimal numberspowers of base 10 are used, for which a 1 is written in the denominator followed by as many zeros as decimal figures the number has, for example:
For pure repeating decimal numbers, the number must be written without the decimal point, and then the number or numbers that are before the period are subtracted. A 9 is placed as a denominator for this result for each digit found before the period, for example:
For mixed repeating decimal numbers, the numerator represents the subtraction of the number omitting the decimal point minus everything before the period. In the denominator, as many 9s are placed as there are digits in the period, followed by as many 0s as there are digits in the pre-period, for example:
Following