Decimal numbers and fractions

A decimal number is any real number that consists of an integer part and a decimal part, which are separated by a comma.

Decimal numbers and fractions

In other words, a decimal number is a real number that we recognize by carrying a comma and can be divided between an integer part and a decimal part.


A fraction is expressed in the form:


Both the numerator and denominator can be numbers or functions. If they were functions that depend on the same variable, we could write it as follows:

Fraction With Functions
Fraction from functions

Decimal number

A decimal number is expressed in the form:

Decimal number
Decimal number

Where e is a whole number and all the following letters d stand for decimal. Therefore, in a decimal number we will always find an integer part. The integer part is the number before the comma. The decimal part is the part after the comma.

Scheme of the structure of a decimal number

Scheme Of A Decimal Number
Scheme of a decimal number

The decimal part is also called the fractional part . So, knowing that it receives this name, we can already think that decimal numbers and fractions share things.

Decimal numbers and fractions

What do decimal numbers and fractions have in common?

Decimal numbers and fractions have so much in common that they become the same mathematical concept but with a different expression. In other words, decimal numbers and fractions are the same but written differently:

Decimal Numbers And Fractions
Decimal numbers and fractions

Let’s prove it

We suppose that we want to write the number 4.5 as a fraction.

First we have to think of two numbers that divided into 4.5. This combination of numbers can be any number. For example, 9 and 2

Example 27

Any equivalent function will result in 4.5.

We obtain 4.5 by dividing 9 by 2, such that:

Fraction And Decimal Number
Fraction and decimal number

So, we see that we can express the same numerical element in two different ways: in function form and in decimal number form.

Example of decimals and fractions

Express the following decimal numbers as a fraction:

Example 28

Given the properties of the fractions, these three examples could be expressed with other equivalent fractions. For example, 3.5 can be the division of 14/4, 28/8, or 112/32. Equivalent fractions are those fractions that are obtained by multiplying the numerator and denominator by the same number.

The solution of the first example is the fraction of 7/2 since it is the irreducible fraction. In other words, it is a fraction that cannot be further reduced equivalently to result in an integer for the dividend and divisor.