Number Theory

# Converting Repeating Decimals into Fractions

Which of the following is equal to $\frac{11}{9}$?

A) $1.1$
B) $1.\overline{1}$
C) $1.2$
D) $1.\overline{2}$
E) $1.9$

Details and assumptions:

$9.\overline{3} = 9.33333...$

\begin{aligned} 0.111111\ldots &= \frac{1}{9} \\ \\ 0.121212\ldots &= \ ? \end{aligned}

Express $1 . 2 \overline{94}$ as a fraction.

Evaluate $\displaystyle{\frac{ 0 . \overline{26} }{ 9 . \overline{7} }}$ by changing the decimals into fractions.

Which of the following is equal to $0.\overline{21}$?

Details and assumptions:

$9.\overline{3} = 9.33333...$

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