What is 3.8 repeating as a fraction in simplest form

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12-09-2017
Mathematics

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What is 3.8 repeating as a fraction in simplest form

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jdoe0001 jdoe0001 · Answer 1 · 2017-09-12T22:33:56+02:00

[tex]\bf 3.8888888\overline{8}\\\\ -------------------------------\\\\ x=3.8888888\overline{8}\qquad thus\qquad \begin{array}{llcll} 10x&=&38.888888\overline{8}\\ &&\downarrow \\ &&35+3.8888888\overline{8}\\ &&\downarrow \\ &&35+x \end{array} \\\\\\ 10x=35+x\implies 9x=35\implies x=\cfrac{35}{9}[/tex]

the idea being, you multiply the "x" by some power of 10 that moves the repeating part to the left of the decimal point and the split it like above.