How do you write 5/9 as a decimal?

The correct answer is: $0.\overline{5}$

Explanation

Dividing 5 by 9 produces a repeating decimal because the remainder repeats during long division. The digit 5 repeats indefinitely, so the decimal is 0.555… which is written $0.\overline{5}$.

Steps:

  1. First step: $$\frac{5}{9}$$
  2. Second step: Long division shows the remainder repeats: $$5.000\ldots\div 9\Rightarrow 0.\text{ (remainder }5)\,,\ \ 50\div 9=5\text{ (remainder }5)$$
  3. Final step: Since the remainder 5 repeats, the digit 5 repeats forever: $$\frac{5}{9}=0.555\ldots=0.\overline{5}$$

Therefore, $5/9$ as a decimal is $0.\overline{5}$.

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