Number Theory
# Rational Numbers

What is $0.1212 \ldots$ in fractional form?

$\frac{n}{ 810} = 0.\overline{d25} = 0.d25d25d25d25\ldots$

For which positive integer $n$, will $d$ be a digit?

$\large \displaystyle {0. \overline{42}-0.\overline{35}= \, ?}$

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**Note:** $0.\overline{ab}=0.abababab \ldots$

Is $0.285714285714\overline {285714}$ rational?

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**Note:** The notation $“\, \overline{285714}"$ indicates that these digits in the decimal are being repeated. For example, $0.1\overline{2} = 0.12222 \ldots.$