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AysviL [449]
2 years ago
6

What is 3.8 repeating as a fraction in simplest form

Mathematics
1 answer:
Olin [163]2 years ago
6 0
\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}

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.
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Step-by-step explanation:

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