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converting recurrent decimals to fractions

methods:

calculator method:

1. insert number with as many decimals as possible

2. press equals sign

eg: 0.7 ˙ = 0.777777777… —> $$\frac{7}{9}$$

eg: 0.6˙3˙ = 0.636363636363… —> $$\frac{63}{99}$$

algebraic method

1. write out the stuffs eg: x = 0.166666666…

2. times by 10 eg: 10x = 1.666666666…

3. subtract these two thingys like so: $$\begin{align*} 10x &= 1.666666666\ldots \\ -\ x &= 0.166666666\ldots \\ \hline 9x &= 1.5 \end{align*} $$

4. then make x = 1 by doing: $$\frac{9x}{9}=\frac{1.5}{9}$$

5. you now have x= $$\frac{1.5}{9}$$

6. simplify to become $$\frac{1}{6}$$