Question

how do you write $-0.overline{72}$ as a fraction?
$-\frac{8}{11}$
$-\frac{6}{11}$
$-\frac{7}{11}$
$-\frac{5}{8}$
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Explanation:

Step1: Let x equal the repeating decimal

Let $x = -0.\overline{72}$, so $x = -0.727272...$

Step2: Multiply x by 100 (2 repeating digits)

$100x = -72.727272...$

Step3: Subtract original x from 100x

$100x - x = -72.727272... - (-0.727272...)$
$99x = -72$

Step4: Solve for x

$x = \frac{-72}{99} = -\frac{8}{11}$

Answer:

$-\frac{8}{11}$ (Option A)