Question

how do you write $-7.8\overline{3}$ as a fraction? $-7\frac{5}{6}$ $-7\frac{7}{9}$ $7\frac{5}{6}$ $7\frac{7}{9}$

Explanation:

Step1: Isolate the repeating decimal

Let $x = 0.8\overline{3}$, so $x = 0.8333...$

Step2: Eliminate repeating decimals

Multiply $x$ by 10: $10x = 8.333...$
Multiply $x$ by 100: $100x = 83.333...$
Subtract $10x$ from $100x$:
$100x - 10x = 83.333... - 8.333...$
$90x = 75$

Step3: Solve for x

$x = \frac{75}{90} = \frac{5}{6}$

Step4: Combine with the integer part

$-7.8\overline{3} = -7 - \frac{5}{6} = -7\frac{5}{6}$

Answer:

$-7\frac{5}{6}$