Question

Express $\frac{1}{9}$ as a repeating decimal, using a bar to indicate the repeating digits.

What are the decimal representations of $\frac{2}{9},\frac{3}{9},\frac{8}{9},\frac{9}{9}$?

Answer 1

Express the fraction in decimal:

The bar is used on the repeating digits.

Divide $1$ by $9$ to express in decimal:

$\begin{array}{rcl}\frac{1}{9}& =& 0.111111\\ & =& 0.1\overline{1}\end{array}$

Where the bar is representing the repeating decimal.

Now, express all the decimals in repeating decimal:

$\begin{array}{rcl}\frac{2}{9}& =& 0.2\overline{2}\\ \frac{3}{9}& =& 0.3\overline{3},\\ \frac{8}{9}& =& 0.8\overline{8}\\ \frac{9}{9}& =& 1\end{array}$

Therefore, all the given number has been represented in decimal with repetition of the decimal.