Question

Convert the decimal $2.83333\dots$ into a fraction

• A. $\frac{19}{7}$
• B. $\frac{17}{6}$
• C. $\frac{14}{5}$
• D. $\frac{13}{5}$

Answer 1

The correct option is B $\frac{17}{6}$

Let, $D=2.83333\dots \left(i\right)$
On multiplying both the sides by $10,$ we get
$\Rightarrow 10D=28.3333\dots \left(ii\right)$
Again,on multiplying both the sides by $10,$ we get
$100D=283.3333\dots \left(iii\right)$
By substracting equation $\left(ii\right)$ from $\left(iii\right),$ we get
$\Rightarrow 90D=255$
$\Rightarrow D=\frac{255}{90}\Rightarrow D=\frac{17}{6}$