Question

How to do a repeating decimal and turn it into it's rational form for example 0.3 repeating??? ​

Answer 1

`\bf 0.\overline{3}\qquad \qquad x=0.\overline{3}\qquad \qquad \begin{array}{llll} 10\cdot x&=&3.\overline{3}\\\\ 100\cdot x&=&33.\overline{3} \end{array}\qquad \qquad \begin{array}{rllll} \stackrel{100x}{33.\overline{3}}\\\\ -\stackrel{10x}{3.\overline{3}}\\ \cline{1-1} 30.0 \end{array} \\\\[-0.35em] ~\dotfill\\\\ 100x-10x=30\implies 90x=30\implies x=\cfrac{30}{90}\implies x=\cfrac{1}{3}`

Answer 2

Step-by-step explanation: 0.3 repeating can be made rational by turning it into 1/3.