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.
See development and solution
Development:
$$a=2,654$$
$$b=13,\widehat{187}$$
$$c=19,13\widehat{76}$$
- 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 $$c$$:
$$\dfrac{1}{100}\cdot 1913,\widehat{76}=\dfrac{1}{100}\cdot \dfrac{191376-1913}{99}=\dfrac{189463}{9900}$$
Solution:
$$a=\dfrac{1327}{500}$$
$$b=\dfrac{13174}{999}$$
$$c=\dfrac{189463}{9900}$$