Question

To convert $0.83$ repeating to a fraction.

Answer 1

Hint: In this question we will use the concept of a fraction as let assume the given number as $x$ and multiply it with $10$. A fraction represented with its quotient and remainder is called a mixed fraction. It is a combination of whole numbers and a proper fraction. A mixed fraction is used to change an improper fraction.

Complete step by step solution:
In this question first, we will discuss the fraction. As we know that A fraction represents a part of the whole. A fraction represented with its quotient and remainder is called a mixed fraction. It is a combination of whole numbers and a proper fraction. A mixed fraction is used to change an improper fraction. The symbol used to represent the fraction is slash /.
Fractions surround our daily activities. The learning of fractions is very useful for anyone to understand algebra later.
There are various ways to learn fractions by performing our daily life activities. A fraction in which the numerator is less than the denominator is called a proper fraction.
A fraction in which the numerator is greater than the denominator is called an improper fraction.
To convert $0.83$ repeating to a fraction let us assume,
$ \Rightarrow 0.83 = x$……. (1)
As we know that $x$ is recurring in one decimal place so multiply it by $10$.
$ \Rightarrow 10x = 8.33$……. (2)
Now we will subtract equation 1 from 2 as,
$ \Rightarrow 10x - x = 8.33 - 0.83$
Now we will simplify the above equation as,
$ \Rightarrow 9x = 7.5$
Now, we will divide both side by $9$ as,
$ \Rightarrow x = \dfrac{{7.5}}{9}$
After simplification we will get,
$\therefore x = \dfrac{5}{6}$

Therefore, the fraction form of $0.83$ is $\dfrac{5}{6}$.

Note: As we know that if the fraction is positive, then it has its own absolute value. Fractions are used in many fields such as in banking, in finding the portion of a whole. Fractions are used to understand the nature of numbers and their interactions.