Answer:
8/45
Step-by-step explanation:
Define x to be the value of your fraction:
[tex]x=0.1\overline{7}\\\\10x=1.7\overline{7}\qquad\text{multiply by 10}\\\\10x-x=1.7\overline{7}-0.1\overline{7}=1.6\\\\x=\dfrac{1.6}{9}=\dfrac{8}{45}\qquad\text{divide by 9; put in lowest terms}[/tex]
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When in doubt, you can use your calculator to see which fraction gives you 0.1777777778.
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We multiplied by 10^1 above, because there is 1 repeating digit. The power of 10 we use matches the number of repeating digits.
