Mathematics: What is 0.612 ( 12 repeating) as a fraction

An equation is when something equals (is the same as) something else, and in mathematics you can see that something is an equation if it has an equals sign or =. So answer 4 is the correct one....

What is 0.612 ( 12 repeating) as a fraction - id0612123461011, michellegregg10

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kiylabeasty7302

08.01.2022

Mathematics

the idea behind the recurring decimal as a fraction, is to first off, multiply or divide by some power of 10, in order that we leave the recurring decimal to the right of the decimal point.

then we multiply by a power of 10, in order to move the repeating digits to the left of the decimal point, anyhow, let's proceed.

$\bf 0.6\overline{1212}\implies \cfrac{06.\overline{1212}}{10}\implies \cfrac{6+0.\overline{1212}}{10}\qquad \qquad \stackrel{\textit{now let's make}}{x=0.\overline{1212}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} 100\cdot x &=& 12.\overline{1212}\\\\ &&12+0.\overline{1212}\\\\ &&12+x\\\\ 100x&=&12+x\\\\ 99x&=&12\\\\ x&=&\cfrac{12}{99}\implies x = \cfrac{4}{33} \end{array} \\\\[-0.35em] ~\dotfill$

$\bf \cfrac{06.\overline{1212}}{10}\implies \cfrac{6+x}{10}\implies \cfrac{6+\frac{4}{33}}{10}\implies \cfrac{~~\frac{202}{33}~~}{10}\implies \cfrac{~~\frac{202}{33}~~}{\frac{10}{1}}\implies \cfrac{202}{330} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{101}{165}~\hfill$

notice, we first divided by 10, to move the decimal point over to the right by 1 slot, then we multiplied by 100, to move it two digits over the decimal point, namely the repeating "12", thus we use 100.

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What is 0.612 ( 12 repeating) as a fraction

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