Rewrite as a simplified fraction.
\[\large{1.\overline{5} = {?}}\]
3 answers
To rewrite the decimal as a fraction, we can set $x=1.\overline{5}$ and multiply both sides of the equation by 10 to move the decimal point one place to the right: $$10x = 15.\overline{5}.$$Subtracting $x$ from both sides, we have $$9x = 15.$$Dividing both sides by 9, we find that $$x = \frac{15}{9} = \frac{5}{3}.$$So, the simplified fraction equivalent to $1.\overline{5}$ is $\boxed{\frac{5}{3}}$.
wrong
To find the fraction equivalent of 1.\overline{5}, we can set $x = 1.\overline{5}$. Multiplying both sides by 10, we have $10x = 15.\overline{5}$. Subtracting the original equation $x = 1.\overline{5}$ from both sides, we get $10x - x = 15.\overline{5} - 1.\overline{5}$, which simplifies to $9x = 14$. Dividing both sides by 9, we have $x = \frac{14}{9}$. Therefore, the simplified fraction equivalent to $1.\overline{5}$ is $\boxed{\frac{14}{9}}$
1 answer