Question

Write 1.1212... as a mixed number

Answer 1

we start off by making the recurring value a variable and then moving the recurring part or digits to the left by multiplying it by some power of 10, now, in this case the recurring digis are just two, 12, so we'd use 10².

`x=1.\overline{121212}\hspace{5em}\boxed{ \begin{array}{llll} 100x&=&112.\overline{121212}\\\\ &=&111+1.\overline{121212}\\\\ &=&111+x \end{array}} \\\\\\ 100x=111+x\implies 99x=111\implies x=\cfrac{111}{99}\implies x=\cfrac{37}{33}\implies x=1(4)/(33)`