From decimal numbers to fractions
Define an exact decimal number $a$, a pure periodic decimal number $b$ and a ultimately periodic decimal number $c$. Find the equivalent fraction of each one.
$$a=2,654$$
$$b=13,\widehat{187}$$
$$c=19,13\widehat{76}$$
- The fraction equivalent to $a$:
$$\dfrac{2654}{1000}=\dfrac{1327}{500}$$
It is not possible to simplify it any more since $500$ only contains the factors $2$ and $5$, and $1327$ cannot be divided by either $2$ or by $5$.
- Equivalent fraction to $b$:
$$\dfrac{13187-13}{999}=\dfrac{13174}{999}$$
And it is not possible to simplify it any more.
- Fraction equivalent to $c$:
$$\dfrac{1}{100}\cdot 1913,\widehat{76}=\dfrac{1}{100}\cdot \dfrac{191376-1913}{99}=\dfrac{189463}{9900}$$
$$a=\dfrac{1327}{500}$$
$$b=\dfrac{13174}{999}$$
$$c=\dfrac{189463}{9900}$$