Question

How do you convert $3.3$ ($3$ repeating) as a improper fraction?

Answer 1

Step-1: Convert the given decimal into fraction:

Let $\mathrm{x}=3.333...$

$\Rightarrow$ $\mathrm{x}=3.\overline{3}$ $...\left(\mathrm{i}\right)$

$\Rightarrow$$10\mathrm{x}=33.\overline{3}$ $...\left(\mathrm{ii}\right)$ [Number of repeating digits after decimal is $1$, so multiply both sides by ${10}^1=10$ ]

Step-2: Subtracting $\left(\mathrm{i}\right)$ from $\left(\mathrm{ii}\right)$:

$10\mathrm{x}-\mathrm{x}=33.\overline{3}-3.\overline{3}$

$\Rightarrow$ $9\mathrm{x}=30$

$\Rightarrow$ $\mathrm{x}=\frac{30}{9}$ [Dividing both sides by $9$]

$\Rightarrow$ $\mathrm{x}=\frac{10}{3}$

Hence, the required improper fraction is $\frac{11}{3}$.