Question

How do you write $4/9$ as a decimal?

Answer 1

Hint: In this question we are given the number $4/9$ which we will first write in the fraction format and then do the division by first multiplying the numerator and denominator by $10$so that we can simplify the expression and perform division and get the required solution.

Complete step by step answer:
We have the given term as $4/9$.
It can be written in the fraction format as:
$\Rightarrow \dfrac{4}{9}$
Now this fraction is in the format of a proper function which means that the numerator is lesser than the denominator.
Now to simplify the division we will multiply both the numerator and denominator of the fraction by $10$ to convert a part of the fraction to an improper in which the numerator is greater than the denominator so that we can divide the part of a fraction.
On multiplying, we get:
$\Rightarrow \dfrac{4\times 10}{9\times 10}$
On simplifying the terms in the numerator, we get:
$\Rightarrow \dfrac{40}{9\times 10}$
Now on rearranging the terms in the fraction, we get:
$\Rightarrow \dfrac{40}{9}\times \dfrac{1}{10}\to (1)$
Now consider the first term in the expression:
$\Rightarrow \dfrac{40}{9}$
Now the first term in the expression can be divided and written as:
$\Rightarrow 4.4444$, which is a recurring term which means that the term $4$ is always repeating. Now on substituting the value in equation $(1)$, we get:
$\Rightarrow 4.4444\times \dfrac{1}{10}$
On simplifying the expression, we get:

$\Rightarrow 0.4444$, which is the required answer.

Note: Different types of fractions should be remembered which are a proper fraction in which the numerator is lesser than the denominator, improper fraction in which the numerator is greater than the denominator and mixed fraction which is a product of a whole number and a fraction.