Question

What is $2\dfrac{1}{3}$ as decimal?

Answer 1

Hint: We first try to explain the improper fraction and the representation in mixed fraction. We use variables to express the condition between those representations. Then we apply long division to express the improper fraction in mixed fraction where we convert the proper fraction part into decimal.

Complete step by step solution:
The given fraction $2\dfrac{1}{3}$ is a mixed fraction.
Let the fraction be $\dfrac{a}{b}$ where $a>b$. Now we express it in the form of mixed fraction. Let’s assume the integer we get is $x$ and the proper fraction is $\dfrac{c}{b}$.
Then the equational condition will be $\dfrac{a}{b}=x+\dfrac{c}{b}$. The representation of the mixed fraction will be $x\dfrac{c}{b}$. We convert the $\dfrac{c}{b}$ part into decimal.
Now we solve our fraction $2\dfrac{1}{3}$. We can express as $2\dfrac{1}{3}=2+\dfrac{1}{3}$.
Therefore, the proper fraction is $\dfrac{1}{3}$. The integer is 2.
Now we find the decimal form of $\dfrac{1}{3}$. We get
$3\overset{0.33...}{\overline{\left){\begin{align}
  & 10 \\
 & \underline{9} \\
 & 10 \\
 & \underline{9} \\
 & 1 \\
\end{align}}\right.}}$
The addition will give $2+0.3333.=2.3333.....$. The round off gives $2\dfrac{1}{3}=2.3$
The decimal of $2\dfrac{1}{3}$ is $2.3333.....$.

Note: We need to remember that the denominator in both cases of improper fraction and the mixed fraction will be the same. The only change happens in the numerator. The relation being the equational representation of $a=bx+c$.