Question

Represent $\mathrm{1.787878787878...}$ in $\frac{p}{q}$ form.

• A. $\frac{59}{99}$
• B. $\frac{59}{33}$
• C. $\frac{33}{59}$
• D. $\frac{59}{66}$

Answer 1

The correct option is B

$\frac{59}{33}$

In $\mathrm{1.7878787878...}$, the block $78$ is repeating after the decimal.

Let $x=1.\overline{78}$ ... (i)

$100x=178.\overline{78}$ ... (ii)

Subtracting equation (i) from (ii), we get,

$99x=177$

$\Rightarrow x=\frac{177}{99}=\frac{59}{33}$