Question

how do you write 0.8overline{3} as a fraction?
options: (\frac{10}{11}), (\frac{7}{10}), (\frac{5}{6}), (\frac{2}{3})

Explanation:

Step1: Analyze each option

• For \(\frac{10}{11}\): Calculate \(10\div11\approx0.909\) (wait, no, wait the repeating decimal is \(0.8\overline{3}\)? Wait, maybe a typo, maybe \(0.8\overline{3}\) is \(0.8333\cdots\). Let's recalculate:
• \(\frac{10}{11}\approx0.909\) (no, wrong). Wait, maybe the decimal is \(0.8\overline{3}\) (83 repeating? Wait, the problem says \(0.8\overline{3}\) (3 repeating). Let's compute each fraction:
• \(\frac{7}{10} = 0.7\)
• \(\frac{5}{6}\approx0.8333\cdots\) (since \(5\div6 = 0.8333\cdots\))
• \(\frac{2}{3}\approx0.666\cdots\)
• Wait, maybe the decimal is \(0.8\overline{3}\) (3 repeating), so \(0.8333\cdots\). Now check \(\frac{5}{6}\): \(5\div6 = 0.8333\cdots\), which matches \(0.8\overline{3}\). Wait, but the first option \(\frac{10}{11}\approx0.909\), no. Wait, maybe the decimal is \(0.8\overline{3}\) (3 repeating). Let's re - evaluate:

Wait, maybe I misread the decimal. If the decimal is \(0.8\overline{3}\) (3 repeating), then:

• \(\frac{5}{6}=0.8333\cdots\), which is \(0.8\overline{3}\).
• \(\frac{10}{11}\approx0.909\), \(\frac{7}{10} = 0.7\), \(\frac{2}{3}\approx0.666\cdots\)

Step2: Match the decimal with the fraction

The decimal \(0.8\overline{3}\) (3 repeating) is equal to \(\frac{5}{6}\) because \(5\div6 = 0.8333\cdots\)

Answer:

\(\frac{5}{6}\) (the third option, C. \(\frac{5}{6}\) if we consider options as A. \(\frac{10}{11}\), B. \(\frac{7}{10}\), C. \(\frac{5}{6}\), D. \(\frac{2}{3}\))